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Teacher Education Students: Their Experienceof Mathematics Anxiety, Self-Efficacy,

and Teacher Professional Development

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Authors Olson, Amy Michelle

Publisher The University of Arizona.

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TEACHER EDUCATION STUDENTS: THEIR EXPERIENCE OF MATHEMATICS ANXIETY, SELF-EFFICACY, AND TEACHER PROFESSIONAL DEVELOPMENT

by

Amy M. Olson

____________________________

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF EDUCATIONAL PSYCHOLOGY

In Partial Fulfillment of the Requirements

For the Degree of

DOCTOR OF PHILOSOPHY

In the Graduate College

THE UNIVERSITY OF ARIZONA

2014

Running Head: TEACHER EDUCATION STUDENTS’ EXPERIENCES 2

THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE

As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Amy Olson, titled Teacher Education Students: Their Experience of Mathematics Anxiety, Self-Efficacy, and Teacher Professional Development and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy.

_______________________________________________________________________ Date: April 25, 2014 Thomas Good _______________________________________________________________________ Date: April 25, 2014 Debora Levine-Donnerstein _______________________________________________________________________ Date: April 25, 2014 Heidi Burross _______________________________________________________________________ Date: April 25, 2014 Darrell Sabers Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. ________________________________________________ Date: April 25, 2014 Dissertation Director: Thomas Good


STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of the requirements for an

advanced degree at the University of Arizona and is deposited in the University Library to be

made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided

that an accurate acknowledgement of the source is made. Requests for permission for extended

quotation from or reproduction of this manuscript in whole or in part may be granted by the head

of the major department or the Dean of the Graduate College when in his or her judgment the

proposed use of the material is in the interests of scholarship. In all other instances, however,

permission must be obtained from the author.

SIGNED: Amy M. Olson


ACKNOWLEDGEMENTS

During my doctoral program, there are many people to whom I wish to express my most

sincere thanks for their support and for the very many things I have learned both from their

instruction and from their example as scholars. I am indebted to my advisor and mentor, Thomas

Good, who not only provided me with professional development opportunities as Research

Coordinator for his project, but also taught me two of the most important lessons that will guide

my future scholarship, the power of “small wins” (Weick, 1984) and the need bring an historical

perspective to our work as researchers. Tom always inspires me with the unique perspective he

brings to his own work and to considering the work of others.

I would also like to express my gratitude to Darrell Sabers, my former advisor and

current mentor. It was Darrell who recruited me to the program and provided me with my first

experiences in educational research. It is through his example that I have begun to appreciate the

value of being a hard-working scholar, caring advisor, and wonderful person, and it is through

his example, that I know that these are goals that I will continue to pursue throughout my career.

I wish to thank my committee and official and unofficial advisors, whose guidance was

instrumental not only in the dissertation process, but throughout my graduate career. Thank you

to Deborah Levine-Donnerstein, for the many statistical meetings that were not only informative,

but also fun opportunities to challenge and deepen my multivariate thinking with an expert in the

field. Thanks also to Heidi Burross, who brought insight about teacher education students to her

reading of my work and who provided opportunities over the years to build my own insight into

teacher education in my work as a teaching assistant in her pre-service courses. Thank you to

Melissa Curran for teaching me the importance of considering children as children (and not just

students), and also for reminding me that no matter how deeply I become steeped in the history


of a theoretical approach or educational paradigm, that it is also important to keep abreast of the

most recent research. I also wish to thank Courtney Koestler and Marcy Wood, who taught me

almost everything I know about mathematics education and also served as absolutely amazing

role models of life in academia. Finally, thank you to Mary McCaslin. Mary provided me with

many opportunities to work with education students, thus shaping both my teaching philosophy

and my research focus. I remain inspired by her work on resilience and self-regulation, and

apply her findings not only to my research, but also to raising my children. In short, I owe many

thanks to the wonderful faculty with whom I have had the opportunity to work so closely with

over my time in the program.

Throughout my program, I have also had the opportunity to work with a number of

wonderful (and oftentimes brilliant) peers. These individuals have become friends and a family

of choice throughout this process, and I wish to thank them all. Most especially, I could not have

managed this last hurdle without the support of Julian Mendez, Ruby Vega, and Elizabeth

Freiberg and without the models of successful graduates like Francesca López, Caroline Wiley,

Alyson Lavigne, and Huaping Sun.

There are a few people I must thank for everything they have done and continue to do to

make life run more smoothly. Many thanks are due to Toni Sollars, for being the person to hold

together the department on a good day and solve each and every crisis on a bad one. And most

especially, I thank my parents, family, and friends. Without these people, I would not have had

the love and support I needed to complete this dissertation.

Finally, this research would not be possibly without the support of the current Algebra

Ready team (Thomas Good, Courtney Koestler, Christine Vriesema, Ganna Sobolevs’ka,

Zachary Hojnacki, and Jacob Davidson), and the contributions of past project team members


(Marcy Wood, Darrell Sabers, Wayne Brent, Elizabeth Freiberg, Ruby Vega, Jennifer Kinser-

Traut, Crystal Kalinec-Craig, Chelsey Earnhart, Lyndah Anderson, Lauren Pierce, Sebastian

Glen, Veronica Atondo, and Jesús Orduño), and advisors (Douglas Grouws, Philip Callahan,

Mathew Felton-Koestler, Jennifer Eli, Huaping Sun, and Alyson Lavigne). Further, Algebra

Ready is funded through a grant from the Helios Education Foundation, and I am especially

appreciative of the support of Jo Anne Vasquez in her role as the project’s Helios advisor.


DEDICATION

To Matt, Jon, and Wil,

for pulling together and supporting me throughout this rigorous and rewarding process,

and for always keeping in mind the Olson Family Motto


TABLE OF CONTENTS

LIST OF FIGURES ...................................................................................................................... 12

LIST OF TABLES ........................................................................................................................ 13

ABSTRACT .................................................................................................................................. 14

CHAPTER 1: INTRODUCTION ................................................................................................. 15

Context of Research .................................................................................................................. 15

Major Theoretical Frameworks and Constructs ........................................................................ 15 Purpose ...................................................................................................................................... 17

Research Questions ................................................................................................................... 18

Organization .............................................................................................................................. 19

CHAPTER 2: LITERATURE REVIEW ...................................................................................... 20

Self-Efficacy Theory ................................................................................................................. 20

Development and Outcomes of Efficacy Beliefs .................................................................. 21 Distinguishing Self-Efficacy from Related Concepts ........................................................... 24

Teacher Efficacy ....................................................................................................................... 27

Teacher Efficacy Outcomes .................................................................................................. 29 General Teaching Efficacy (Outcome Expectancies) ........................................................... 30 Collective Teaching Efficacy ................................................................................................ 31 Improving Teacher Efficacy ................................................................................................. 32

Mathematics Anxiety ................................................................................................................ 34

Defining Mathematics Anxiety ............................................................................................. 34 Mathematics Anxiety and Students ...................................................................................... 35 Mathematics Anxiety of Pre-Service Teachers ..................................................................... 35


Mathematics Anxiety of In-Service Teachers ....................................................................... 37 Connecting Teachers and Students ....................................................................................... 38 Mathematics Anxiety and Self-Efficacy ............................................................................... 39

Objectives and Research Questions .......................................................................................... 41

Descriptive Questions ........................................................................................................... 41 Model Questions ................................................................................................................... 42

Learning Block Participation Questions ............................................................................... 44

CHAPTER 3: DATA AND METHODS ...................................................................................... 46

Materials ................................................................................................................................... 46

Participants ................................................................................................................................ 47

Procedure .................................................................................................................................. 48

Sources of Data ......................................................................................................................... 48

CHAPTER 4: RESULTS .............................................................................................................. 54

Demographics ........................................................................................................................... 54

Reliability of Scales .................................................................................................................. 55

Descriptive Statistics ................................................................................................................. 56

Mathematics Anxiety Measures ............................................................................................ 56 Self-Efficacy Measures ......................................................................................................... 58 Outcome Expectancies .......................................................................................................... 60

Model Analyses ........................................................................................................................ 63

Diagnostics: Tests of Assumptions ....................................................................................... 63 Model 1: Grade Level Preference ......................................................................................... 67 Model 2: Subject Area Preference ........................................................................................ 69


Analysis of Learning Block Participation ................................................................................. 76 Selection into Learning Block Participation ......................................................................... 76 Experience with Learning Blocks ......................................................................................... 77 Response to Learning Blocks................................................................................................ 78

CHAPTER 5: DISCUSSION ........................................................................................................ 87

Summary of Findings ................................................................................................................ 87

Self-Efficacy ......................................................................................................................... 87

Mathematics Anxiety ............................................................................................................ 89 Outcome Expectancies .......................................................................................................... 90 Model 1 ................................................................................................................................. 90

Model 2 ................................................................................................................................. 91

Experience with Professional Development ......................................................................... 92

Theoretical Implications ........................................................................................................... 95

Self-Efficacy Theory ............................................................................................................. 95

Mathematics Anxiety Construct ........................................................................................... 96

Practical Implications................................................................................................................ 97

Self-Efficacy ......................................................................................................................... 97

Mathematics Anxiety ............................................................................................................ 98 Outcome Expectancies .......................................................................................................... 98

Limitations .............................................................................................................................. 100

Future Directions .................................................................................................................... 102

Conclusion .............................................................................................................................. 103

APPENDIX A: RECRUITMENT AND CONSENT DOCUMENTS ....................................... 105


Initial Recruitment Email ........................................................................................................ 105

Follow-Up Recruitment Email ................................................................................................ 106 Teacher Education Student Consent Form ............................................................................. 107

APPENDIX B: COMPLETE INSTRUMENTATION ............................................................... 109

Learning Block Review Items ................................................................................................ 109 Survey ..................................................................................................................................... 111

REFERENCES ........................................................................................................................... 119


LIST OF FIGURES Figure 1: Model of the Development and Outcomes of Self-Efficacy based on Bandura's Theory

............................................................................................................................................... 24

Figure 2: General Outcome Expectancy as a Contributor to the Social Persuasion Pathway in

the Development of Self-Efficacy .......................................................................................... 27

Figure 3: Mathematics Anxiety as a Contributor to the Physiological Arousal Pathway in the

Development of Self-Efficacy ................................................................................................ 40

Figure 4: Model 1: Self-Efficacy as a Mediator of the Relationship between Mathematics Anxiety

for Learning, Mathematics Outcome Expectancies, and Grade Level Preference .............. 43

Figure 5: Model 2: Self-Efficacy as a Mediator of the Relationship between Experience (Mastery

and Vicarious), Outcome Expectancies (Teacher and Student), Mathematics Anxiety, and

Subject Area Preference for Mathematics ............................................................................ 44

Figure 6: Revised Model 1: Self-Efficacy for Learning Mathematics as a Mediator in the

Relationship between Anxiety for Learning Mathematics and Grade Level Preference ...... 67

Figure 7: Non-Significant Predictors in the Relationship between Anxiety for Learning

Mathematics, Self-Efficacy for Learning Mathematics, and Grade Level Preference ......... 69

Figure 8: Revised Model 2: Relationship between Anxiety for Teaching Mathematics, Outcome

Expectancies for Teaching Mathematics, Self-Efficacies for TEaching Mathematics, and

Subject Area Preference for Mathematics ............................................................................ 70

Figure 9: Significant Predictors in the Relationship between Vicarious Experience, Mathematics

Teaching Anxiety, Self-Efficacy for Teaching Mathematics, and Subject Area Preference for

Mathematics .......................................................................................................................... 75


LIST OF TABLES

Table 1: Characteristics of Teacher Education Students as a Percentage of the Sample ............ 54

Table 2: Reliability of Self-Efficacy, Mathematics Anxiety, and Outcome Expectancy Scales for

Total Sample at Time 1 (N = 53) and Time 2 (N = 22) ........................................................ 55

Table 3: Exploration of Assumptions of Univariate Skewness, Kurtosis, and Normality ............ 65

Table 4: Correlations and b Coefficients for Logistic Regression of Mathematics Learning

Anxiety (MAL) and Self-Efficacy for Learning Mathematics (SELM) as Predictors of Grade

Level Preference .................................................................................................................. 69

Table 5: Correlations and b Coefficients for Standard Multiple Regression of Self-Efficacy for

Teaching Variables (SESE, SEIS, SETM) on Subject Area Preference for Mathematics .... 72

Table 6: Correlations and b Coefficients for Standard Multiple Regression of Experience (ME,

VE), Mathematics Teaching Anxiety (MAT), and Outcome Expectancies for Teachers (OET)

on Self Efficacy for Teaching Mathematics (SETM) ............................................................ 73

Table 7: Mean Differences from Time 1 to Time 2 in Self-Efficacy, Mathematics Anxiety, and

Outcome Expectancy Variables with Participation in Learning Blocks .............................. 77

Table 8: Mean, Standard Deviation, and Mode of Teacher Education Student and In-Service

Teahcer Responses to Learning Blocks ................................................................................ 79

Table 9: Learning Block Feedback: Major Themes and Responses from In-Service Teachers and

Teacher Education Students ................................................................................................. 81


ABSTRACT

This dissertation adds to the teacher education literature by exploring the experiences

education students have of mathematics anxiety and self-efficacy for teaching and learning

mathematics. Further, the utility of a specific in-service teacher professional development

project, focused on improving rational number instruction, in pre-service education is evaluated,

and the potential impact of professional development experiences on the anxieties and efficacy

beliefs of students before they enter the teaching profession is explored. This study provides

evidence of the predictive capacities of teacher efficacy models that incorporate student

experiences and feelings of anxiety to better understand task choice. For example, findings

indicate that self-efficacy for teaching mediates the relationship between mathematics teaching

anxiety, experience, and mathematics subject area preference for teacher education students.

Further, there are indications of the potential for teacher education coursework and in-service

teacher professional development to decrease students’ experience of mathematics teaching

anxiety. Finally, evidence is provided that teacher professional development is not only

perceived as useful to teacher educations students, but has potential as an intervention for teacher

efficacy and anxiety for teaching. Given these findings, it makes sense to further evaluate the

ways in which the strengths of pre-service coursework and in-service professional development

can be leveraged to best prepare future teachers for their professional roles. Further research is

also needed to longitudinally track experiences of anxiety and self-efficacy as students leave

teacher education and enter the classroom as professionals.

Keywords: self-efficacy, teacher efficacy, mathematics anxiety, teacher education,

mathematics education, teacher professional development


CHAPTER 1: INTRODUCTION

Context of Research There is currently a great deal of focus on improving teacher education, particularly as

research begins to accumulate to demonstrate the economic, time, and skills costs of low teacher

retention (e.g., Henry, Bastian, & Fortner, 2011; Kersting, Chen, & Stigler, 2012; Sawchuk,

2013). When teacher turnover is high, the professional field becomes populated with novices.

This introduces challenges not only for the new teachers, but also for the students they will work

with and administrators who will be responsible for their professional development and

retention. Novices are, by definition, much different from experts in the ways they approach

problems, the degree to which they understand the available supports, and the degree to which

they persevere when faced with setbacks. Thus, it is important to understand how novices

approach their first experiences in the field and investigate what can be done to help them be

better prepared and more resilient to potential failures as they develop their skill sets.

Major Theoretical Frameworks and Constructs This study is situated in the self-efficacy theoretical framework. Self-efficacy is a

context-specific estimation individuals have of their abilities to organize and execute particular

goals to a desired level of success. Self-efficacy is not a global estimation of ability or

confidence; individuals hold many efficacy beliefs that reflect their perceptions of different types

of skills and the contexts in which they feel more or less confident (Bandura, 1997). Efficacy

beliefs guide motivation and behavior, including task choice, effort, persistence, and resilience

(Schunk & Pajares, 2005).


Self-efficacy is developed with respect to four types of experiences: mastery, vicarious,

social persuasion, and physiological arousal (Bandura, 1997). Mastery experiences occur when

individuals successfully perform particular skill sets. Vicarious experiences occur when

individuals observe others engaged in mastery experiences. Social persuasion includes verbal

messages, particularly of encouragement or discouragement of the possibility of meeting goals.

Physiological arousal occurs when the body experiences stress. The physical reactions can be

interpreted as positive or negative, and interpretation impacts how physiological arousal

influences efficacy.

This study relates to a particular type of efficacy belief called teacher efficacy: beliefs

teachers hold with regard to their “capabilities to bring about desired outcomes of student

engagement and learning, even among those students who may be difficult or unmotivated”

(Tscahnnen-Moran & Woolfolk Hoy, 2001). As explained in Chapter 2, a large body of research

links teacher efficacy to both teacher behaviors and student outcomes.

In efficacy theory, mastery experiences are considered the most direct evidence of

efficacy and thus, have the most influence on an individual’s efficacy beliefs (Bandura, 1997).

However, this study is situated in the context of novice teachers and thus, the other pathways to

the development of efficacy are important. For example, observations of mentor teachers and

teacher education faculty (potential sources of vicarious experience), anxiety related to learning

and teaching content (potential sources of physiological arousal) and outcome expectancies

related to the relative ease or difficulty of teaching tasks (potential sources of social persuasion)

are investigated in this study.

The link between teacher efficacy and experience of mathematics anxiety is also explored

in this study. Mathematics anxiety may be a general fear of mathematics or a more specific fear


of failing in mathematics (Hembree, 1990; Trujillo & Hadfield, 1999). The experience of

mathematics anxiety interferes with both mathematical learning and willingness to engage in

mathematical behaviors, including teaching (Gresham, 2007; McGlynn-Stewart, 2010). A large

body of research indicates that mathematics anxiety and low self-efficacy are prevalent in the

pre-service teacher population (Beilock, Gunderson, Ramirez, & Levine, 2010; Brown,

McNamara, Hanley, & Jones, 1999; Bursal & Paznokas, 2006; Harper & Daane, 1998; Hembree,

1990; Peker, 2009; Rech, Hartzel, & Stephens, 1993; Swars, Daane, & Giesen, 2006; Tooke &

Lindstrom, 1998; Vinson, 2001). This is potentially problematic for the purpose of improving

teacher education students’ transition to the professional field as teachers, especially given the

large body of empirical evidence linking mathematics anxiety, student outcomes, and teacher

behaviors. This is further discussed in Chapter 2.

Purpose

The study presented here attempts to investigate ways in which novice teacher education

students, particularly those interested in teaching elementary grades, experience constructs

known to impact the behaviors of pre-service and in-service teachers (i.e., mathematics anxiety

and teacher efficacy beliefs), both as students in teacher education faculty’s classrooms and in

their own classrooms as future teachers. Further, this study investigates the utility of

professional development materials created for in-service teachers to be used as part of pre-

service education. The purpose of this portion of the study is to discover if materials can be

successfully adapted to use with teacher education students and if these students have different

needs than in-service teachers.


Research Questions The research questions guiding this study are presented here and more fully explained at

the end of Chapter 2. Hypotheses are also presented in Chapter 2.

1. To what extent do teacher education students experience:

a. self-efficacy for teaching and learning mathematics?

b. mathematics anxiety around the teaching and learning of mathematics?

c. positive or negative perceptions of outcome expectancies related to teachers,

students, and mathematics content?

2. Does self-efficacy for learning mathematics content mediate the relationship between

anxiety for learning mathematics content, outcome expectancies about mathematics

content, and preferred grade level?

3. Does self-efficacy for teaching mathematics content mediate the relationship between

mastery experiences, vicarious experiences, outcome expectancies about teachers and

students, mathematics teaching anxiety and subject area preference for mathematics?

4. Does experience with teacher professional development (learning blocks) act to reduce

mathematics anxiety, increase self-efficacy, and improve the positivity of outcome

expectancies?

5. Are there initial quantitative differences on the survey responses between those students

who choose to complete the learning blocks and those students who do not?

6. Are there qualitative differences in the responses to learning block material between this

group of teacher education students and the previously collected responses of in-service

teachers?


Organization As described earlier, Chapter 2 presents the literature review, research questions, and

relevant hypotheses. In Chapter 3, the methods and procedure are presented. This chapter also

includes information about the participants, instruments, and other data sources. Chapter 4

presents analysis, including analyses of reliability, descriptive statistics, regression models, mean

comparisons, and qualitative findings. In Chapter 5, the results are summarized and explained.

Theoretical and practical implications are discussed. The limitations are evaluated, and future

directions are considered.


CHAPTER 2: LITERATURE REVIEW

This literature review covers two constructs important to understanding teacher education

students teaching beliefs and behaviors. First, self-efficacy theory is discussed, both generally

and in relation to the research in teacher efficacy. Next, mathematics anxiety is introduced as a

measure of physiological arousal believed to be particularly influential with the population of

teacher education students and in-service teachers, especially those interested in teaching

elementary grades. These constructs are used to build research questions that are defined at the

end of this section.

Self-Efficacy Theory

In attempting to explain why the effectiveness of social cognitive treatment varied by

individual, Bandura (1977) argued that behavioral and psychological change was reliant on

motivational variables. In particular, the belief that individuals have in their ability to

successfully make a psychological or behavioral change predicts whether or not they will do so.

He called this concept “self-efficacy.”

Self-efficacy is a context-specific estimation individuals have of their abilities to organize

and execute particular goals to a desired level of success. While there may be some overlap of

efficacy beliefs between spheres of activity that require similar skill sets, an individual’s efficacy

is not a global belief and cannot be measured as a single trait. As Bandura (2006) explains, “One

cannot be all things, which would require mastery of every realm of human life. People differ in

the areas in which they cultivate their efficacy and in the levels to which they develop it even

within their given pursuits” (p. 307). Thus, individuals hold many self-efficacy beliefs that

reflect different types of skills and different contexts. Further, individuals within the same

context, such as pre-service and in-service teachers, vary in the their final estimation of their own


self-efficacies based on their individual experiences with specific goals in particular contexts.

The specificity and malleability of self-efficacy beliefs makes this theoretical approach useful in

attempting to understand how individuals function in particular contexts, and how individuals’

beliefs about themselves and their abilities change over time as they progress from novices to

masters in particular contexts.

Development and Outcomes of Efficacy Beliefs

Within a context, self-efficacy is theorized to develop through four general pathways:

mastery experiences, vicarious experiences, social persuasion, and physiological arousal

(Bandura, 1997). These pathways are depicted in Figure 1 and explained here. Mastery

experiences occur when the individual successfully practices and/or performs particular skills.

Vicarious experiences build on Bandura’s model of observational learning, and include those

experiences in which the individual observes others engaging in the practice or performance of

relevant skills. As in observational learning, when the individual identifies with the model,

observing success will increase self-efficacy and observing failure will decrease self-efficacy.

Social persuasion includes encouragement (or discouragement) of the possibility of meeting

particular goals. Social persuasion can be delivered in different ways and at different times. For

example, a “pep talk” before performance and feedback after performance are both considered

forms of verbal persuasion. Just as the extent to which vicarious experiences affect self-efficacy

depends on the degree to which the individual identifies with the model, social persuasion varies

in effect based on the credibility, trustworthiness, and expertise of the persuader (Bandura,

1986). Physiological arousal refers to the body’s reaction to stressful or threatening conditions.

Interpretation of these bodily cues as aversive leads to decreases in self-efficacy, while

interpretation as excitement may increase self-efficacy.


It seems important to further consider the role of physiological arousal, as a potentially

underexplored facet of the development of self-efficacy for novices. Physiological arousal is

described as the physical effects the body experiences in a potentially situation, but in terms of

development of self-efficacy, the emphasis is placed on the interpretation of these effects rather

than the experience itself (Bandura, 1997). Thus, it is the perception of, for example, increased

heart rate as excitement or fear that increases or decreases self-efficacy. These physical triggers

happen most often in concert with the performance of a mastery experience or the contemplation

of a potential mastery experience (given that self-efficacy is a forward-looking judgment). To a

lesser extent, physiological arousal may occur when watching others perform a task (vicarious

experience) or when receiving warnings or encouragement about a task (social persuasion). Of

particular interest in the development of self-efficacy with novices who have little mastery

experience to draw upon, is the experience of task-specific physiological arousal, and in

particular, anxiety related to engaging in specific tasks or to the contemplation of tasks, a point

which will be further expanded upon later in this section.

The theory suggests that self-efficacy is altered as the individual gains further

experiences relevant to the four developmental pathways. Because of their direct experiential

nature, mastery experiences are theorized to be the most important influences for the

development of self-efficacy (Bandura, 1997). Thus, past experiences of one’s own success do

much more to improve self-efficacy than the observation of another person being successful,

encouragement that one has the potential to be successful, or excitement going into the task. In

the same way, past experiences of failure are profoundly inhibiting to the development of

positive self-efficacy. Though not as explicit in the theory, the other three sources of influence

(i.e., vicarious experience, social persuasion, and physiological arousal) are theorized to more


strongly influence the development of an individual’s self-efficacy when the individual is in the

early stages of developing efficacy beliefs (i.e., is a novice) and has few mastery experiences on

which to make judgments of future ability.

Once self-efficacy beliefs are established, they are expected to be fairly stable unless

some unusual experience or upheaval requires reassessment. Thus, efficacy is most variable in

the novice stages of building context-specific ability sets. However, even after the novice stage,

Bandura (2006) argues that powerful mastery experiences may even influence “transformational

restructuring of efficacy beliefs…across diverse realms of functioning” (p. 308), which suggests

that important successes can potentially give individuals powerful boosts of confidence, even

when past experiences of failure have led them to have low self-efficacy. Likewise, important

failures can also decimate healthy self-efficacy. It is this focus on the vicarious experiences,

social persuasion, and physiological arousal of novices and the importance of scaffolding

powerful (and successful) mastery experiences that makes self-efficacy useful in understanding

influential aspects of training programs, such as pre-service education.


Figure 1

Model of the Development and Outcomes of Self-Efficacy based on Bandura’s Theory

Figure 1 also depicts the expected outcome of efficacy beliefs. Motivation, effort, and

persistence in the face of challenge are all linked to self-efficacy (Bandura, 1993). Individuals

who believe they will (eventually) be successful are more likely to initially engage in tasks, put

in more effort, and persevere if difficulty arises. A good deal of research in classroom settings

further suggests that individuals with high self-efficacy are more likely to select challenging

goals and use appropriate self-regulation strategies to reach these goals (e.g., see Bandura &

Locke, 2003; Pajares, 1996; Schunk, 1990; Zimmerman, 2000; Zimmerman, Bandura, &

Martinez-Pons, 1992).

Distinguishing Self-Efficacy from Related Concepts

Self-efficacy differs from actual competence (capacity for success), because self-efficacy

is a perception of future ability to succeed, rather than an evaluation of one’s actual skill level


(Woolfolk Hoy & Spero, 2005). Individuals regularly over- and underestimate their future

competence. Chronic low self-efficacy for particular tasks impedes individuals from engaging in

these tasks, while high self-efficacy increases individuals’ likelihood of engaging in tasks.

However, inaccurately high self-efficacy sets an individual up for frustration and failure. Thus

self-efficacy estimates slightly higher than actual competence are healthiest for approaching new

goals (Bandura, 1997).

Self-efficacy also differs from outcome expectancy, or the more general belief that

particular actions will result in the desired outcome, regardless of who takes those actions

(Bandura, 1977). Recall that self-efficacy was initially defined as a person- and context-specific

belief that the individual can be successful in making a psychological or behavioral change.

Outcome expectancies frame the difficulty of making those changes for the general person.

Most commonly, outcome expectancies are framed in contrast to self-efficacy (e.g.,

Pajares, 1996; Zimmerman, 2000). Yet, although not explicitly modeled in the theory, relevant

general outcome expectancies should also influence one’s own self-efficacy beliefs by increasing

or decreasing (or perhaps even not changing) the perceived difficulty of an individual achieving

a successful outcome. In other words, they frame the perceived difficulty of making changes in

particular contexts. Further, outcome expectancies may be communicated amongst groups via

social persuasion (Bandura, 1993). Thus, outcome expectancies should be modeled along with

self-efficacy, particularly when the work is with novices who have few mastery experiences to

draw upon in formulating their efficacy beliefs.

An illustration is provided here to further demonstrate the relationship between outcome

expectancies and the lower efficacy beliefs of novices. A novice teacher would be expected to

have lower levels of self-efficacy for preparing students for an important high-stakes test than a


veteran teacher. Prior to any mastery experiences (classroom experiences of preparing students

for high-stakes tests) or even vicarious experiences (observing a mentor teacher prepare students

for high-stakes tests), the novice would likely hold outcome expectancies (e.g., that preparing for

high-stakes tests is relatively easy or difficult for teachers, relatively easy or difficult for

students, relatively important or unimportant for student, teacher, or school success, and so

forth). It seems likely that these outcome expectancies would influence how the novice

interpreted the physiological arousal cues when entering into a first potential mastery experience.

For example, the arousal cue of increased heart rate would be more likely to be interpreted as

anxiety or nervousness when the task was initially believed to be difficult and important.

Thus, general outcome expectancies act as perceptions of the general difficulty or ease of

success in a particular context. They may be based on preconceived notions, social persuasion,

or prior learning of social messages, but they are general judgments, and not specific to the

individual and thus, often depicted as outside the self-efficacy model. However, it seems likely

there is some relationship between general outcome expectancies and self-efficacy. A person

with high self-efficacy may perceive a task as simpler than a person with low self-efficacy, but

the relationship does not seem absolute. For example, a teacher may have high self-efficacy for

classroom management tasks based on past mastery experiences at a previous school. At the

school where she is comfortable, she may rate the general outcome expectancy of classroom

management for any teacher as relatively easy. However, at a new school, different

environmental cues or social messages from fellow teachers could cause her to perceive the task

(or the students) as potentially more difficult in general for all teachers, and this perception

seems likely to influence her personal self-efficacy to engage in classroom management


outcomes. This relationship is depicted in Figure 2, in which general expectancies become part

of the social persuasion pathway and thus predict self-efficacy.

Figure 2

General Outcome Expectancy as a Contributor to the Social Persuasion Pathway in the

Development of Self-Efficacy

Teacher Efficacy The development of self-efficacy, particularly for novices, is of interest because of the

situation of this work in the the teacher education context. Research suggests that 40% of

teachers leave within their first five years of teaching (Gold, 1996), but this is also about the

same amount of time it seems to take for teachers to progress from novices to effective teaching

masters (Henry, Bastian, & Fortner, 2011; Kersting, Chen, & Stigler, 2012). Thus, the

educational context is populated with novice teachers in need of developing self-efficacy for

skills associated with long-term student achievement and motivation.


Based on self-efficacy theory, a definition of teacher efficacy would reflect the beliefs an

individual teacher has of future competence using a particular teaching skill. However, like

most educational research, the impetus is to link teacher efficacy with student achievement.

Thus, Tschannen-Moran and Woolfolk Hoy (2001) offer the following definition: “A teacher’s

efficacy belief is a judgment of his or her capabilities to bring about desired outcomes of student

engagement and learning, even among those students who may be difficult or unmotivated” (p.

783). Like self-efficacy, teacher efficacy is context-specific and multi-dimensional construct,

and is expected to reflect judgments on a variety of behaviors associated with students’ academic

outcomes.

Also like self-efficacy, teacher efficacy is theorized to arise from four developmental

sources (mastery experiences, vicarious experiences, social persuasion, and physiological

arousal). Tschannen-Moran & Woolfolk Hoy (2007) provide evidence and examples of each of

these four pathways for novice and “career” teachers. For example, novice teachers have

powerful mastery experiences when they conduct a lesson they perceive to be successful. These

experiences have a much less powerful impact on the more experienced career teachers, who

have more stable self-efficacy due to a longer history of mastery experiences. Student teaching

is filled with vicarious experiences as pre-service teachers work with teacher education faculty

and in-service teachers in their classrooms, and indeed, “Teachers entering the field have

typically experienced ‘apprenticeships’ of at least 17 years as students”, suggesting the

importance of modeling by professors and cooperating teachers within teacher certification

programs as well as the importance of students’ earlier experience in elementary and secondary

classrooms (p. 954). Supporting communications from colleagues and the community are

important sources of social persuasion, but novice teachers who rely too greatly on these have


lower efficacy beliefs than teachers who rely less on input from others (Tschannen-Moran &

Woolfolk Hoy, 2007). Although Tchannen-Moran and Woolfolk Hoy (2007) do not explicitly

describe it, communication of negative expectations from colleagues, supervisors, parents, and

the community about teachers, students, and achievement should also decrease the efficacy of

novice teachers. Physiological arousal may indicate excitement and anticipation for an

upcoming lesson or may indicate unhappiness, anxiety, or stress with the teaching experience,

but teacher stress is more often studied in relation to academic futility, burnout, and other

constructs designed to get at low levels of teacher retention in the field (e.g., Friedman, 2000;

Skaalvik & Skaalvik, 2007 ).

Teacher Efficacy Outcomes

Teacher efficacy is widely explored in the literature; as would be expected by the

necessity of pre-service education and in-service professional development, there is interest in

understanding a) how teacher efficacy develops throughout a teacher’s training and career and b)

what, if any, impacts can be made on teacher efficacy at various stages in order to support

teachers as they transition from novices to career professionals.

Historically, teacher efficacy was first linked with student achievement in a series of

RAND studies (Armor, et al., 1976) and to student motivation in the following decade (e.g.,

Anderson, Greene, & Lowen, 1988; Midgley, Feldlaufer, & Eccles, 1989). Across the decades

of research, teacher efficacy has also been linked to a number of observable “good teaching”

behaviors and “best practices”, such as teacher planning, organization, time on subject, positive

management and instructional strategies, and lower referral rates to special education (Allinder,

1994; Meijer & Foster, 1988; Riggs & Enochs, 1990; Soodak & Podell, 1993; Woolfolk, Rosoff,

& Hoy, 1990). Ross (1998) reviewed the first two decades of literature on teacher efficacy and


summarized that teacher efficacy was positively associated with six behaviors necessary to be

successful in the classroom: (1) learning to use new teaching strategies, (2) using classroom

management strategies that encourage student autonomy rather than assert teacher control, (3)

providing targeted assistance to low-achieving students, (4) building students’ perceptions of

their own academic skills, (5) setting attainable goals in the classroom, and (6) persisting even

when students fail. Ross’s work aligns well with Bandura’s (1993) framework that efficacy

outcomes can be summarized with respect to task choice (i.e., goal-setting, enacting particular

strategies), motivation and effort (i.e., to continue learning new strategies and to put effort into

classroom interactions), and persistence and resilience (particularly in cases of student failure or

underachievement).

More recently, teacher efficacy theorists have extended early work to look beyond

student effects and begun exploring the effects of teachers’ efficacy beliefs on their professional

behaviors and willingness to continue in the field. For example, recent work provides evidence

that efficacious teachers hold more positive goals and aspirations for their own work in the

classroom (Muijs & Reynolds, 2002; Woolfolk Hoy & Spero, 2005) and are also less likely to

burnout and leave the field (Friedman, 2000; Skaalvik & Skaalvik, 2007).

General Teaching Efficacy (Outcome Expectancies)

Historically, there was some confusion between teacher efficacy (sometimes referred to

as “personal teaching efficacy”) and the arguably misnamed concept of “general teaching

efficacy". General teaching efficacy is an outcome expectancy related to the teachers’ general

beliefs about the possibility of making changes in student achievement or motivation given

context variables. For example, general teaching efficacy might refer to a teacher’s beliefs about

the possibility of helping improve student success within the context of student variables like


socioeconomic level, ethnicity, home language, and so forth (Tournaki & Podell, 2005). These

general outcome expectancies frame the difficulty (or ease) of success for teachers in the

classroom, and thus, are consistent with the outcome expectancy variable that was hypothesized

earlier to be particularly influential for novices.

Collective Teaching Efficacy

In recent years, researchers have begun to measure teacher efficacy as a school-level

variable (collective efficacy), and evidence for the link between collective efficacy and student

achievement is starting to accumulate (Goddard, 2001; Goddard & Goddard, 2001; Goddard,

Hoy, & Woolfolk Hoy, 2000, 2004; Tschannen-Moran & Barr, 2004; Tschannen-Moran &

Woolfolk Hoy, 2007). Like self-efficacy, collective efficacy is a belief about the capability a

group has to organize and execute particular goals (Tschannen-Moran & Woolfolk Hoy, 2007).

It is especially relevant to teaching as teachers work together within school units to reach shared

goals (e.g., school is “passing” or academically successful), and these schools are headed by

administrative leaders (principals), who are responsible for supporting and evaluating the

teachers within particular school units. Teachers within a school have access to similar

resources, supports, limitations, and budgets. Schools often serve particular populations of

students, and by nature of their work together, teachers receive vicarious experiences and social

persuasion from other teachers and administrators within the schools that may affect teacher

efficacy via the social transmission of general outcome expectancies, which in turn can affect the

perceptions of collective efficacy for the school. Goddard, Hoy, and Woolfolk Hoy (2004) argue

that collective efficacy creates normative pressure for teachers to push towards school-level

expectations for success, but whether these expectations are positive or negative may depend on

other school-level variables.


Interestingly, Woolfolk Hoy and Spero (2005) found that while teacher efficacy and

general teacher efficacy (outcome expectancy for teachers) increased across pre-service

education, measures of general teaching efficacy dropped significantly between the end of

student teaching and the end of the first year of in-service teaching. In fact, these measures

dropped to the point at which they were at the beginning of pre-service training, indicating that

any improvements in general outcome expectancies made in pre-service education were lost

when teachers entered the field and become immersed in particular schools.

Thus, some aspect of fieldwork must impact novices’ general outcome expectancies.

This paper presents the argument that one source of the detrimental shift is the social

transmission of negative outcome expectancies within the school unit. Novices are particularly

at risk to be influenced by messages produced in a climate of low collective efficacy because of

their unstable efficacy beliefs. Further, if novices have unrealistically high efficacy beliefs

supported throughout their pre-service education program, their first difficulties in mastery

settings may serve to reinforce negative messages from peers and administrators. More work is

needed to understand the complex relationship between novice efficacy beliefs and the social

messages and collective efficacies of the schools in which novices teachers are placed.

Improving Teacher Efficacy

Further, given the recent focus on teacher education reform (Sawchuk, 2013) and the

economic and skills costs of low teacher retention (Henry, Bastian, & Fortner, 2011; National

Commission on Teaching and America’s Future, 2003; 2007), it has become increasingly

important to develop positive, but realistic, teacher efficacy in pre-service education and support

continued positive efficacy beliefs once teachers enter the field. Evidence suggests that it is

possible to increase teacher efficacy in pre-service education by providing powerful mastery


experiences during student teaching and in the induction year (Mulholland & Wallace, 2001;

Woolfolk Hoy & Spero, 2005). However, researchers also caution against establishing

unrealistic efficacy beliefs in pre-service education, particularly when these beliefs may lead to

disillusionment and burnout when they are not supported by early mastery experiences in the

classroom (Friedman, 2000).

There is also a body of work demonstrating that in-service teacher efficacy can be

affected by professional development efforts. For example, Zambo and Zambo (2008)

demonstrated improvements in teacher efficacy (but not in collective efficacy) following a

summer workshop on mathematics problem solving. Ross and Bruce (2007) found that efficacy

for a particular teaching behavior, student management, increased following a semester of

mathematics skill training, even though more general measures of personal teaching efficacy did

not. JohnBull and Hardiman (2013) compared teachers who participated in a cross-curricular

intervention over the summer and over a semester. They found that teachers who participated in

the longer program improved in both teacher efficacy and outcome expectancy, while teachers in

the shorter program improved in only teacher efficacy. Similarly, Fritz, Miller-Heyl, Kreutzer,

and MacPhee (1995) found that making impacts in personal teacher efficacy was easier than

making changes in outcome expectancies. The evidence suggesting that personal efficacy beliefs

are the first to change may imply predictive relationships between personal efficacy and

collective efficacy. Further, the difficulty in making and maintaining changes in teacher

outcome expectancies supports the argument that outcome expectancies arise from the

interaction between the community and the individual and that working to change the

individual’s beliefs without changing the social messages in the larger community (i.e., the

school or program) will not be as effective.


Mathematics Anxiety

Defining Mathematics Anxiety

In addition to teacher efficacy, the construct of mathematics anxiety is of interest in this

study. Brady & Bowd (2005) caution that mathematics anxiety is a complex phenomenon

defined in multiple ways across multiple fields, and this is true to a point. However, most

scholars take one of two perspectives. The first perspective is wholly concerned with the

negative physiological sensations associated with anxiety when mathematical tasks are

undertaken. Tobias (1978) referred to this as almost a feeling of “sudden death” when

confronted with mathematics, but most perspectives are less dramatic. The major themes range

from an “unhealthy mood” when actually engaged in mathematics problems (Luo, Wang, & Luo,

2009, p. 12) to a more general “fear of contact with mathematics” (Hembree, 1990, p. 34). The

concern is that these negative physiological feelings disrupt the ability to process information

and thus, disrupt learning and performance (Gresham, 2007).

The second perspective goes beyond the physiological and emotional responses to

anxiety to focus more on the effects that anxiety has on an individual’s self-beliefs. This

perspective argues that mathematics anxiety is a negative physiological response that occurs not

when mathematical tasks are undertaken, but rather when they are perceived to be threatening to

one’s self-esteem (Cemen, 1987 as cited in Trujillo & Hadfield, 1999). Thus, while some

researchers believe than any mathematical stimuli can elicit anxiety, others believe that anxiety is

only induced when individuals are in position of losing self-esteem, confidence, or self-efficacy

in response to failure feedback.

A recent study of the Program for International Student Assessment (PISA) data suggest

that the highest levels of mathematics anxiety occur among students in high-performing nations,

such as Korea and Japan (Lee, 2009). This finding lends support to the Cemen (1987) and


Trujillo and Hadfield (1999) definition of mathematics anxiety, one that is more closely tied to

the potential impact of failure on self-beliefs than to absolute success or achievement.

Mathematics Anxiety and Students

Mathematics anxiety can occur in academic and non-academic, real-world settings

(Jones, Childers, & Jiang, 2012; Newstead, 1998), but it has primarily been examined in the

context of interference with performance and learning in academic settings (Gresham, 2007).

Often, a developmental approach is taken in order to understand how and why some students

move from relatively low levels of anxiety in early schooling to relatively high levels of anxiety

in secondary or post-secondary education. For example, researchers have found that

mathematics anxiety increases significantly between elementary and secondary school (Brown,

McNamara, Hanley, & Jones, 1999; Jackson & Leffingwell, 1999; Trujillo & Hadfield, 1999).

Those students who experience anxiety become increasingly unlikely to continue on in advanced

mathematics when offered the option. Further, both Hembree’s (1990) and Ma’s (1999) meta-

analyses show significant negative relationships between students’ experience of mathematics

anxiety and their mathematics achievement within a course and across schooling.

Mathematics Anxiety of Pre-Service Teachers

Research indicates that mathematics anxiety is particularly prevalent among teacher

education students (Bursal & Paznokas, 2006; Brown et al., 1999; Hembree, 1990; Peker, 2009;

Rech, Hartzell, & Stephens, 1993), and especially with teacher education students interested in

teaching primary grade levels (Beilock, Gunderson, Ramirez, & Levine, 2010; Peker, 2009). In

fact, both Beilock et al. (2010) and Hembree (1990) report that elementary education students,

primarily women, have the highest level of mathematics anxiety of all college majors. This

raises the question of whether students select into the elementary education major because they


have high mathematics anxiety for learning mathematics in general and for participating in

majors that they perceive require more advanced mathematics coursework. If this is the case, it

may be that there exists an inverse relationship between grade level that pre-service teachers

want to teach at and their level of mathematics anxiety.

Moreover, a body of research links this mathematics anxiety in pre-service teachers to

negative outcomes. For example, mathematics anxiety in teacher education students has been

associated with negative attitudes about mathematics and required mathematics courses and with

preference for learning direct instruction methods and traditional algorithms over conceptual

thinking (Brady & Bowd, 2005; Grootenboer, 2008). Similarly, Rayner, Pitsolantis, and Osana

(2009) have demonstrated that lower mathematics anxiety scores in pre-service teachers are

associated with higher performance in mathematics methods courses, and specifically in

conceptual and procedural fraction content.

However, for teachers or potential teachers, Vinson (2001) cautions that mathematics

anxiety is more than simply “not liking” mathematics or being reluctant to teach it. In recent

years, researchers have begun to distinguish between mathematics anxiety in general (i.e.,

anxiety around learning and performing mathematics), from the tension teachers experience

when they encounter real or perceived deficits in their competence to teach mathematics (Peker,

2009). This second phenomenon is referred to as mathematics teaching anxiety. Thus, pre-

service and in-service teachers may suffer from both general mathematics anxiety and anxiety

for teaching mathematics. Further, both types of anxiety are hypothesized to arise from similar

sources – negative experiences with mathematics teachers in their own past (Brady & Bowd,

2005; Stoehr, Carter, & Sugimoto, 2013; Uusimaki & Nason, 2004). For example, Brady &

Bowd (2005) found that teachers recalled experiences of being humiliated by mathematics


teachers perceived to be uncaring or hostile, or feeling embarrassed for making errors in front of

peers, and that these measures were related to their concerns about engaging in mathematics

tasks and teaching mathematics.

It would be incorrect to assume that the two types of anxiety are synonymous; Brown,

Westenkow, and Moyer-Packenham (2011) found that 35.9% of the pre-service teachers in their

sample experienced one type of anxiety without the other (39.6% experienced neither type and

20.8% experienced both types of anxiety). However, little of the wide body of research with pre-

service teachers distinguishes between the two types of mathematics anxiety in order to examine

the potential differential effects they may have on teacher education.

Mathematics Anxiety of In-Service Teachers

Like the research with pre-service teachers, there are relatively few studies that attempt to

disentangle mathematics teaching anxiety from more general mathematics anxiety with in-

service teachers. A notable exception is a study by Hadley and Dorward (2011). They measured

both and found that general mathematics anxiety was significantly, but not perfectly, correlated

with mathematics teaching anxiety (r = .42, p < .001). In their sample, teachers reported greater

levels of general mathematics anxiety (52%) than mathematics teaching anxiety (36%). They

also found a small, but positive relationship between general mathematics anxiety and use of

standards-based teaching practices from the National Council of Teachers of Mathematics and a

small, but negative relationship between mathematics teaching anxiety and student achievement.

As an explanation for this seeming contradiction, Hadley and Dorward argue that teachers who

are anxious about understanding the mathematics, but comfortable with teaching in general, are

more likely to stick closely to recommended practices and approved lesson plans. Teachers who


are more anxious about the instructional aspects tend to rely more on worksheets and direction

instruction.

Most studies with in-service teachers measure general mathematics anxiety, but report on

teaching behaviors. Like the research with pre-service teachers, there are associations between

mathematics anxiety and less skilled teaching (Gresham, 2007; Karp, 1991; Vinson, 2001;

Swars, Smith, Smith, & Hart, 2007). In particular, teachers who score high on mathematics

anxiety measures spend less instructional and planning time on mathematics, are less likely to

develop students’ conceptual thinking, and are more likely to rely on whole-class instruction

with heavy emphasis on drilling and worksheets (Bush, 1989; McGlynn-Stewart, 2010; Vinson,

2001).

Connecting Teachers and Students

Based on work with in-service teachers, it is clear that there is a link between the

mathematics anxiety of teachers and the eventual mathematics achievement of their student due

to poor teaching and/or lack of time spent on mathematical content that teachers feel ill-prepared

to teach. However, this is not the only pathway by which students can be affected by their

teachers’ mathematics anxiety. Mathematics anxiety can also impact students via observation of

the teachers’ anxious behaviors. Evidence suggests that highly anxious teachers perpetuate not

only their anxiety, but also negative attitudes and beliefs about mathematics for their students

(Beilock et al., 2010; Brady & Bowd, 2005; Vinson, 2001), thereby affecting student

achievement not only through poor teaching, but also through students’ lack of motivation and

achievement behavior in mathematics. In terms of self-efficacy theory, it may be that the

mathematics anxiety of teachers results in modeling vicarious experiences and providing social

persuasion that in turn affects students’ efficacy beliefs about their own mathematics capabilities.


Mathematics Anxiety and Self-Efficacy

As argued earlier, the Cemen (1987) and Trujillo and Hadfield (1999) definition of

mathematics anxiety reflects the relationship between the anxiety response and perceptions of

self-beliefs, and thus, provides support for the connection between mathematics anxiety and self-

efficacy, a form of self-belief. From efficacy theory, mathematics anxiety is a source of

physiological arousal that impedes the development of positive self-efficacy. Importantly, Lee

(2009) found in the PISA study that mathematics anxiety and self-efficacy for mathematics were

independent predictors of mathematics performance, indicating the need to measure them

separately, and to assess the degree to which self-efficacy may mediate the relationship between

mathematics anxiety and achievement.

Thus, in this study, mathematics anxiety is investigated as a potential source of negative

physiological arousal that impacts, but is not synonymous with, self-efficacy for teaching and

learning mathematics (Figure 3). Based on the literature, teacher education students, pre-service

teachers, and in-service teachers are expected to experience relatively high levels of mathematics

anxiety. To the extent that teacher education students feel this anxiety, discomfort, unhealthy

mood, or fear when confronted with contemplation of teaching in mathematics (or learning the

mathematics content and pedagogy deeply enough to be effective in teaching mathematics), their

experience of self-efficacy for teaching mathematics should be negatively impacted.


Figure 3

Mathematics Anxiety as a Contributor to Physiological Arousal Pathway in the Development of Self-Efficacy

Research with pre-service and in-service teachers further documents associations

between mathematics anxiety and self-efficacy for teaching mathematics (Bursal & Paznokas,

2006; Swars, Daane, & Giesen, 2006). Typically, higher mathematics anxiety is associated with

lower self-efficacy for teaching mathematics. However, there are some indications that

experiences gained in mathematics education methods courses can help decrease general

mathematics anxiety (Gresham, 2007; Harper & Daane, 1998; Tooke & Lindstrom, 1998;

Vinson, 2001). There is little research into the dosage needed to reduce mathematics anxiety and

little evidence for the duration of positive effects. There is also little research distinguishing the

various effects of anxiety and self-efficacy for teaching mathematics from anxiety and self-

efficacy for learning mathematics during teacher education.


Objectives and Research Questions

In this study, the self-efficacy of teacher education students is investigated with reference

to the specific contexts of learning mathematics content knowledge necessary for successfully

teaching mathematics (i.e., through a teacher education program) and teaching mathematics in

classrooms (with focus on teaching behaviors, instructional strategies, and student engagement).

Mastery experiences (experiences of teaching and related teacher behaviors in real

classrooms) and vicarious experiences (experiences of observing mentor teachers, teacher

education faculty, and so forth) are expected to impact self-efficacy for teaching mathematics.

Outcome expectancies relevant to general ease or difficulty for teachers and students to

make changes in student achievement are assessed. Additionally, outcome expectancies about

mathematical content are also assessed. These measures are used to model beliefs that teacher

education students have as they prepare to enter the classroom and are expected to arise from

social messages.

Mathematics anxiety is used as a proxy for one type of physiological arousal associated

with teaching in mathematics classrooms. Mathematics anxiety is distinguished between

learning (general) and teaching contexts. Given the uncertainty in defining the construct about

whether it is the mathematical content itself or the concern of potential failure associated with

that content, each anxiety measure has embedded items relevant to evaluation.

Descriptive Questions

1. To what extent do teacher education students experience:

a. self-efficacy for teaching and learning mathematics? Are there particular areas

(items) that suggest strong or weak efficacy beliefs?


Hypothesis 1a: Based on theory and the empirical literature, teacher education

students are novices and should experience relatively low levels of self-efficacy

for teaching and learning mathematics.

b. mathematics anxiety around the teaching and learning of mathematics? Are there

particular areas (items) that suggest high or experiences of anxiety?

Hypothesis 1b: Based on the literature, teacher education students should

experience high levels of mathematics anxiety for teaching and learning

mathematics.

c. positive or negative perceptions of outcome expectancies related to teachers,

students, and mathematics content? Are there particular areas (items) that suggest

students hold particularly positive or negative expectations?

Hypothesis 1c: The literature suggests that the positivity of outcome expectancies

peaks during pre-service teacher education and then declines when teachers enter

the professional field. Thus, the hypothesis states that teacher and student

expectancies should be positive. In contrast, more negative outcome expectancies

related to mathematics content are expected given the high levels of anxiety and

low levels of self-efficacy these students are hypothesized to have. Further, low

student expectations may also be evident if these teacher education students see

themselves as students (and thus, perceive that it is difficult to make positive

student achievement gains in mathematics) rather than as teachers.

Model Questions

2. Does self-efficacy for learning mathematics content mediate the relationship between

anxiety for learning mathematics content and preferred grade level.


Hypothesis 2: Students with higher mathematics anxiety and more negative outcome

expectancies about mathematics content will have lower self-efficacy, which will in turn

predict preference to teach at earlier grade levels as depicted in Figure 4.

Figure 4

Model 1: Self-Efficacy as a Mediator of the Relationship between Mathematics Anxiety for

Learning, Mathematics Outcome Expectancies, and Grade Level Preference

3. Does self-efficacy for teaching mathematics content mediate the relationship between

mastery experiences, vicarious experiences, outcome expectancies, mathematics anxiety,

and subject area preference for mathematics?

Hypothesis 3: Students with more mastery experiences, more vicarious experiences, more

positive outcome expectancies (teachers and students), and lower mathematics anxiety

will have higher self-efficacy, which will in turn result in greater preference for teaching

mathematics, as depicted in Figure 5.


Figure 5

Model 2: Self-Efficacy as a Mediator of the Relationship between Experience (Mastery and

Vicarious), Outcome Expectancies (Teacher and Student), Mathematics Anxiety, and Subject

Area Preference for Mathematics

Learning Block Participation Questions

4. Does experience with teacher professional development (i.e., Algebra Ready learning

blocks) act to reduce mathematics anxiety, increase self-efficacy, and improve the

positivity of outcome expectancies? Is it more difficult to make changes in some

constructs than others?


Hypothesis 4: Learning block experience will improve student ratings of self-efficacy and

outcome expectancies and decrease ratings of mathematics anxiety. Based on the

literature, it will be most difficult to improve outcome expectancies.

5. Are there initial quantitative differences between differences on the survey responses

between those students who choose to complete the learning blocks and those students

who do not?

Hypothesis 5: Students with higher self-efficacy and lower mathematics anxiety will be

most willing to complete learning blocks.

6. Are there qualitative differences in the responses to learning block material between this

group of teacher education students and the previously collected responses of in-service

teachers? For example, do teacher education students make different suggestions for

improvement, request different additional materials, or have different affective responses

to the learning blocks than teachers who are already in the classroom?

This question is highly exploratory and thus, no hypothesis is made.


CHAPTER 3: DATA AND METHODS

Materials Professional development materials used in this project came from the Algebra Ready

Project (https://algebraready.oia.arizona.edu). Algebra Ready is a program developed by faculty

from the Department of Educational Psychology, the Department of Teaching Learning, and

Sociocultural Studies, and the Office of Instruction and Assessment at the University of Arizona.

The purpose of the project is to provide high-quality teacher professional development in the

form of online modules (i.e., “learning blocks”). Learning blocks are designed to improve the

instruction of rational numbers (fractions, decimals, and percents) and early algebra concepts

(ratios, rates, proportions, equations, and growth functions) in elementary and middle school.

They are informed by best practice recommendations from the National Council of Teachers of

Mathematics (2000), the National Mathematics Advisory Panel (2008), the National Research

Council (2001), and the Common Core State Standards (National Governors Association Center

for Best Practices, Council of Chief State School Officers, 2010).

Teacher professional development materials used in this study came from two Algebra

Ready learning blocks: Absolute and Relative Reasoning and Key Ideas. These learning blocks

are among the more conceptual learning blocks that have been created. They both focus on basic

concepts that undergird the learning and instruction of rational numbers, and thus, were

specifically chosen to be useful to education students as they complete their studies. While more

applied learning blocks are available, they often ask teachers to try out activities in their

classrooms and report back. The teacher education students do not have the same access to

students as in-service teachers, and thus the more applied blocks were deemed less appropriate

for this audience. Both of the learning blocks used in this study reference fractions, decimals,


and percents and also provide video of quality teaching that may serve as vicarious experience of

rational number lessons for the participating pre-service teachers.

Participants Participants included 53 teacher education students enrolled in courses through the

College of Education (CoE) at the University of Arizona. Initial recruiting was done with

permission of the Dean’s Office and involved CoE faculty posting recruitment documents to two

student listservs (pre-education student listserv and pre-service teacher listserv). After two

weeks, these initial documents were followed up with a secondary recruitment document. With

the permission of the instructors, the author additionally recruited from three courses enrolling

undergraduate teacher education students.

Additional data were drawn from the feedback of in-service teachers who participated in

the learning blocks in the academic year prior to this study. Twenty-four teacher education

students, 21 in-service teachers, and 1 in-service Noyce teacher provided feedback to the

Absolute and Relative Reasoning learning block. Twenty-two teacher education students, 15 in-

service teachers, and two in-service Noyce teachers provided feedback to the Key Ideas learning

block. Noyce Arizona Master Teachers of Mathematics were recruited in the spring prior to this

study. These teachers represent an especially skilled sample of mathematics teachers who

experience a wide range of professional development as part of their participation in the Noyce

Scholars program. The Noyce program is funded by the National Science Foundation with the

goal of increasing the number of science and mathematics teachers prepared to teach in high-

needs schools.


Procedure

Full recruitment and consenting documentation are presented in Appendix A. At the time

of recruitment, potential participants were informed that they would complete two surveys about

their feelings about mathematics and evaluate two online professional development lessons

created by the Algebra Ready Project. They were additionally informed that they would be paid

for their time and feedback. At the time of consenting, they were informed that the total pay

would be $50 for their work on both the surveys and the learning blocks. The work was

expected to take less than three hours, and in most cases, students took approximately two hours

to complete all work.

Upon consent, teacher education students completed the first survey, which is described

in greater detail in the next section. Once the survey was completed, they were provided with

login information to the Algebra Ready website, where they gained access to all existing learning

blocks. They were specifically asked to review the two learning blocks described earlier.

Within each learning block, there are embedded feedback questions. Additional items are

presented after completion of a learning block.

Once both learning blocks were completed, teacher education students were emailed a

link to the final survey. They were also provided with information necessary for arranging

payment for their work.

Sources of Data

Prior to gaining access to the learning blocks and after completing the two assigned

learning blocks, participants completed a survey that assessed self-efficacy for teaching and

learning mathematics, mathematics anxiety, and outcome expectancies related to mathematics

instruction as related to content, students, and teachers. At pretest, the survey also included


some demographic information. At posttest, the self-efficacy, mathematics anxiety, and outcome

expectancy items were reassessed, and students were also given the opportunity to provide any

final thoughts or feedback about their experience with the learning blocks and with the project in

general. Full copies of the survey are presented in Appendix B. The following sections describe

the source and intent of the items presented in the surveys.

Self-Efficacy

Some items were drawn from the Teachers’ Sense of Efficacy Scale – short form

(Tschannen-Moran & Woolfolk Hoy, 2001). This instrument is widely used and has well-

documented measurement parameters. All scale reliabilities are reported as α ≥ 0.81. This

instrument provides a connection with recent studies with both pre-service and in-service

teachers. It was initially designed at Ohio State University to reflect the concerns of teacher

education faculty, and thus, the content validity is established in terms of teacher education

goals. It has also been used in longitudinal work to look at teacher induction, retention, and

professional development (e.g., Tschannen-Moran & Woolfolk Hoy, 2007; Woolfolk Hoy &

Spero, 2005). The survey consists of three scales (Student Engagement, Instructional Strategies,

and Classroom Management). In particular, the Student Engagement and Instructional Strategies

scales were used in this study. Some items were adapted to reflect the mathematics focus of this

study (e.g., replacing the more general “school work” with “math”).

Consistent with the Bandura (1997) definition of self-efficacy these items reflect specific

tasks that teachers must do (e.g., craft good questions, implement alternative strategies, motivate

students). Participants are asked to rate “how much” or “how well” they will be able to do these

tasks when they enter the classroom.


Additional self-efficacy items have been drawn from the Mathematics Teaching Efficacy

Beliefs Instrument (MTEBI, Enochs, Smith, & Huinker, 2000), a revision of the Science

Teaching Efficacy Beliefs Instrument (STEBI, Riggs & Enochs, 1990) to reflect mathematics

content. Unlike the STEBI, the MTEBI is written to reflect future perceptions of teaching as it

was intended to be used with pre-service teachers, and thus, is more closely aligned to the

Bandura (1997) theoretical definition of self efficacy as a forward-looking judgment of future

capability.

Like the STEBI, the MTEBI measures two factors; the instruments are designed based

on the Gibson and Dembo (1984) approach to measuring teacher efficacy beliefs and thus,

provides measures of both personal teacher efficacy and general teacher efficacy (outcome

expectancy). By providing scales for both, the MTEBI and STEBI allows the user to investigate

the relationship between the more specific personal teacher efficacy (α = .88 for the MTEBI and

.92 for the STEBI) and the beliefs or outcome expectancies (α = .75 for the MTEBI and .77 for

the STEBI) about the general difficulty (or ease) of teaching in general (i.e., the extent to which

teacher education students believe teachers can have an effect on student outcomes).

When Enochs, Smith, and Huinker (2000) created the MTEBI, they removed some

STEBI items that were related to outcome expectancies about students (e.g., The low science

achievement of some students cannot be blamed on their teachers.). The rationale for doing so

was to keep the focus cleanly on what they called teacher general efficacy by removing items

that placed the locus for achievement on students. However, these general efficacy statements

about students seem to capture beliefs that teachers hold that frame the relative ease or difficulty

of making changes in students’ achievement given the characteristics of students.


Thus, the items that were removed when the MTEBI was created from the STEBI have

been included in this study (with minor edits to shift from science to mathematics focus), and

five additional items were written to frame the ease or difficulty around the locus of mathematics

content rather than teacher or student (e.g., It is more difficult to improve in math than in other

subjects.). The intention was to examine if these items form three separate indicators of outcome

expectancies.

The validity for MTEBI was demonstrated by using confirmatory factor analysis to test

the model (Enochs, Smith, & Huinker, 2000) and for the STEBI, validity evidence was

additionally demonstrated by correlations between the scales and variables such as years spent

teaching subject, choice to teach subject, teacher self-rating, and principal rating of effective

teaching (Riggs & Enochs, 1990).

Mathematics Anxiety

General mathematics anxiety measures were drawn from the Revised Mathematics

Anxiety Scale. The original Mathematics Anxiety Rating Scale (MARS, Richardson & Suinn,

1972) was a very widely used measure throughout the 1970s, but considerable problems with the

instrument resulted in two popular revisions in the 1980s. The major issue with the MARS was

its length (98 items). However, Alexander and Martray (1989) also reported concerns that the

original instrument assumed unidimensionality of the construct despite evidence that two or three

separate constructs were present. A revised and much shortened two-factor solution (24-item

MARS-R, Plake & Parker, 1982) and a three-factor solution (25-item RMARS, Alexander &

Martray, 1989) both gained popularity of use with U.S. undergraduate students. Advances in

confirmatory factor analysis methodology in recent years has allowed better evaluation of these

resulting instruments and further revision, validation, and cross-validation with undergraduate


populations. The Baloğlu and Zelhart (2007) revision of the Alexander & Martray (1989) retains

three reliable scales: Mathematics Text Anxiety, Numerical Task Anxiety, and Mathematics

Course Anxiety. This version has been used with pre-service and in-service teachers (e.g.,

Wilson, 2012, 2013).

The Hopko (2003) revision of the Plake and Parker (1982) MARS-R retains two reliable

scales: Learning Mathematics Anxiety and Mathematics Evaluation Anxiety. This version has

also been used in work with pre-service teachers, and of particular interest given the nature of the

learning blocks, with pre-service teacher anxiety around fractions (e.g., Rayner, Pitsolantis, &

Osana, 2009). It has also been used with in-service teachers and in connecting teacher scores to

student achievement in teachers’ classrooms (e.g., Hadley & Dorward, 2011).

Many of the items for the two instruments overlap, but the emphasis on anxiety for

learning mathematics in the Hopko (2003) revision as opposed to the emphasis on performance

of simple mathematical tasks (addition, subtraction, multiplication, and division) in the Baloğlu

and Zelhart (2007) revision make it a more appropriate choice for this study. Additional items

measure come from Hadley and Dorward (2011). These items are revisions of the Hopko (2003)

items to reflect anxiety about teaching and being evaluated as a teacher of mathematics instead

of learning and being evaluated as a student of mathematics. These are written as consistent with

the MARS-R scales (Hopko, 2003).

Mathematics Proficiency

No attempt was made to assess the students’ mathematics proficiency. This was a

conscious decision on the part of the researcher to make the study appealing to a wider audience

of teacher education students. The literature seems clear that this population is highly anxious

about mathematics. In order to make the final learning blocks most useful to both pre-service


and in-service elementary and middle school teachers, it is important to capture the needs of a

population of students known for high anxiety and low self-efficacy. Thus, no mathematics

achievement or proficiency measures that might invoke anxiety were included. However, even

with these precautions, it is likely that students who were more comfortable with mathematics

content were more likely to participate. The supporting evidence for this belief as well as the

implications of this finding will be discussed later.

Learning Block Feedback and Evaluation

Finally, the participants completed feedback items embedded in the learning blocks.

Complete feedback items are presented with the other instrumentation in Appendix B. In

general, the purpose of the feedback was to assess the utility of the learning blocks for use by

teacher education students and pre-service teachers (e.g., What were the two or three most

helpful ideas that were presented in this learning block? Is the material presented in the learning

block useful to you? Does this learning block provide content that would be useful to pre-service

teachers?). Additional feedback questions probed how the students would make use of the

material (i.e., What are one or two things you will do with this information?) and if they needed

further support or additional materials or explanations to fully utilize the content (i.e., Is there

anything else you would like to know?). These same feedback items have also been presented to

in-service teachers during the iterative design process through which the learning blocks were

created. These questions were included for the purpose of informing project personnel of any

specific needs for targeted audiences of the final materials.


CHAPTER 4: RESULTS

Demographics In order to better understand the results and their generalizability of those results,

demographic information is reported in Table 1 as total sample and participating subsample that

elected to complete learning blocks. The sample represents the group of teacher education

students interested in teaching early and upper elementary grades. The most preferred subject

area to teach was science. English language arts was the least preferred subject area to teach,

perhaps indicating that participation in the project was less appealing to students who preferred

reading to mathematics. Most participants were either in the first or third year of their teacher

education programs. As expected, more teacher education students had vicarious experience of

observing others teach than had mastery experience of creating and teaching their own lessons.

Table 1

Characteristics of Teacher Education Students as a Percentage of the Sample

Characteristic Total (N = 53)

Participants (N = 22)

Preferred Subject Area English Language Arts 17.3 13.0 Mathematics 21.2 26.1 Science 36.5 26.1 Social Studies 23.1 30.4 Preferred Grade Level Early elementary (K-3) 39.6 34.8 Upper elementary (4-5) 45.3 47.8 Middle school (6-8) 3.8 4.3 High school 11.3 13.0 Years in Teacher Education Program Not yet admitted 7.5 14.3 1st year 33.3 28.6 2nd year 12.5 21.4 3rd year 25.0 21.4 4th year 12.5 14.3 Experiences with Mathematics Teaching Taken mathematics classes like those they expect to teach 97.8 100.0


Observed teachers giving mathematics lessons 75.5 78.3 Observed teacher education faculty giving mathematics lessons 49.1 47.8 As a student teacher, assisted a mentor teacher with mathematics lessons

35.8 26.1

Designed mathematics lessons 30.2 39.1 As a student teacher, gave own mathematics lessons 20.8 26.1 Participated in mathematics teacher professional development 15.1 17.4

Reliability of Scales Prior to analysis, the reliability of the four self-efficacy scales (learning, teaching,

instructional strategies, student engagement) the two mathematics anxiety scales (learning,

teaching), and the three outcome expectancy scales (teacher, student, content) were evaluated to

ensure that scales were internally consistent and appropriate to use for analysis. The reliability

of the scales is reported in Table 2. All scales had high reliability (α > .72) except for two

outcome expectancy scales (OES, OEM). Given the low reliability of these scales, they were not

entered into model analysis.

Table 2

Reliability of Self-Efficacy, Mathematics Anxiety, and Outcome Expectancy Scales for Total

Sample at Time 1 (N = 53) and Time 2 (N = 22)

Item Average

Scale Percent

Scale Item Source

k Time α M SD M SD

Self-Efficacy to Learn Mathematics Knowledge for Teaching (SELM)

MTEBI (Enochs, Smith, & Huinker, 2000)

4

1 .679 4.16 .49 83.11 9.72

2 .662 4.25 .46 85.00 9.26

Self-Efficacy to Teach Mathematics (SETM)


8

1 .845 3.84 .64 76.75 12.84

2 .846 3.90 .59 78.07 11.72


Self-Efficacy for Instructional Strategies in Mathematics (SEIS)

TSES (Tschannen-Moran & Woolfolk Hoy, 2001)

4

1 .886 7.16 1.34 79.51 14.89

2 .916 7.13 1.40 78.03 14.87

Self-Efficacy for Supporting Student Engagement in Mathematics (SESE)

TSES (Tschannen-Moran & Woolfolk Hoy, 2001)

4

1 .852 6.93 1.15 77.04 12.80

2 .884 7.03 1.05 77.27 12.82

Mathematics Learning Anxiety (MAL)

MARS-R (Hopko, 2003)

12

1 .909 2.40 .83 47.99 16.55

2 .911 2.30 .81 45.91 16.17

Mathematics Teaching Anxiety (MAT)

MARS-R (Hadley & Dorward, 2011)

11

1 .924 2.50 .85 49.85 16.86

2 .913 2.26 .79 45.21 15.86

Outcome Expectancies for Teachers in Mathematics (OET)


8

1 .715 3.57 .47 71.37 9.47

2 .786 3.71 .47 73.75 9.90

Outcome Expectancies for Students in Mathematics (OES)

STEBI (Riggs & Enochs, 1990)

4

1 .426 3.25 .58 65.09 11.62

2 -.065 3.25 .43 65.00 8.59

Outcome Expectancies for Mathematics Content (OEM)

OEM Olson (2014)

5

1 .302 2.83 .45 56.52 9.05

2 -.038 2.81 .38 56.18 7.56

Descriptive Statistics

Mathematics Anxiety Measures

One intention of this study was to explore the extent to which teacher education students

at the University experience mathematics anxiety and self-efficacy around teaching and learning

mathematics, as well as their perceptions of the relative ease or difficulty of making changes in


student achievement in mathematics with reference to perceptions of teachers, students, and

mathematical content. Thus, some purely descriptive analysis is presented in this section. In

order to make comparisons clearer, student responses were compared to the initial (raw) item

Likert-like scale descriptors as well as transformed to the same metric (percentage of total

possible points). Table 2 provides average item values and percent scores across scales. Effect

sizes for comparisons use Cohen’s h, an effect size measure appropriate to use with proportions

(Cohen, 1988).

On average at Time 1, teacher education students rated their anxiety for learning

mathematics at 47.99% of the total possible score and their anxiety for teaching mathematics at

49.85% of the total possible score, indicating only a very small difference between students’

anxiety for learning mathematics and students’ anxiety for teaching mathematics (h = .04).

Based on percentage scale scores, students tended to respond with anxiety to slightly less than

half of the items on the scales. Anxiety measures were rated on a five-point scale from a low

anxiety score of 1 (“not at all”) to a high anxiety score of 5 (“very much”). The average scores

on the mathematics anxiety items fell between “a little” and “a fair amount” on both the learning

scale (M = 2.40, SD = .83) and the teaching scale (M = 2.50, SD = .84).

In terms of both learning and teaching, anxiety was highest for items that were set in

evaluation contexts [e.g., Teaching: “Preparing students for a ‘standardized’ math test throughout

the week before” (M = 3.13, SD = 1.18), “Waiting for the results of your students’ year-end math

tests” (M = 3.19, SD = 1.14), “Having a surprise evaluation by an administrator during a math

lesson you are teaching” (M = 3.45, SD = 1.17); Learning: “Thinking about an upcoming math

test one day before” (M = 3.19, SD = 1.29), “Taking an examination (quiz) in a math course” (M

= 3.21, SD = 1.26), “Waiting to get a math test returned in which you expected to do well” (M =


3.15, SD = 1.34), “Being given a “pop” quiz in math class” (M = 3.49, SD = 1.23)]. The lowest

levels of anxiety occurred in contexts that attempted to elicit review or studying behaviors [e.g.,

Teaching: “Looking through the pages in your math series teachers’ manual” (M = 1.89, SD =

.99); Learning: “Looking through the pages in a math text” (M = 1.64, SD = .98), “Watching a

teacher work an algebraic equation on the black board” (M = 1.81, SD = 1.09), “Picking up a

math textbook to begin working on an assignment” (M = 1.85, SD = .98)]. Note that these low-

anxiety prompts are most often set in passive context in which the teacher education student is

not yet engaged in mathematics tasks or evaluation of mathematics performance. Teacher

education students also reported relatively low levels of anxiety for a potentially challenging

teaching situation [“Talking to a student who wanted to use a different way to solve a math

problem than the way you taught in class” (M = 1.83, SD = 1.11)], while other teacher

responsibilities were rated as more anxiety-inducing [e.g., “Preparing to teach students a new

math concept that will be challenging for them” (M = 2.74, SD = 1.16), “Explaining the rationale

for the math curriculum to a parent who stopped by your classroom after school” (M = 2.63, SD

= 1.16). Given that teachers are increasingly expected to make data-driven decisions in their

instruction, it is disheartening that the learning item referencing statistics coursework (“Signing

up for a statistics course”) is rated above the mean for anxiety (M = 2.96, SD = 1.49).

Self-Efficacy Measures

Items drawn from the MTEBI (Enochs, Smith, & Huinker, 2000) were used to measure

self-efficacy to learn the content necessary to teach and self-efficacy to engage in teaching

mathematics. At Time 1, teacher education students rated their self-efficacy for learning

mathematics knowledge at 83.11% of the total possible score and their self-efficacy for teaching

mathematics at 76.75% of the total possible score, indicating they felt more efficacious for


learning than they did for teaching (h = .16). However, in both measures, the efficacy beliefs of

teacher education students were quite high; students expressed high levels of agreement that they

will be able to learn and teach content. These items are rated on a five-point agreement scale,

then reverse coded, such that the scale ranged from a low self-efficacy score of 1 (“strongly

disagree” with an efficacy statement) to a high self-efficacy score of 5 (“strongly agree” with an

efficacy statement). Item averages indicate that students tended to fall between “agree” and

“strongly agree” with statements about their efficacy to learn, while they fell somewhere

between “uncertain” and “agree” on statements about their efficacy to teach.

Teaching items that teacher education students responded to with particularly strong

efficacy include “I will typically be able to answer students’ math questions” (M = 4.26, SD =

.66) and “I will generally teach math ineffectively”, which was reverse coded indicating that

teacher education students felt they would be able to teach math effectively (M = 4.19, SD = .76).

In contrast, teacher education students demonstrated lower efficacy when responding to items

like “I wonder if I have the necessary skills to teach math” [reverse coded] (M = 3.23, SD = 1.22)

and “Even if I try very hard, I will not teach math as well as I will most subjects” [reverse coded]

(M = 3.47, SD = 1.20). However, even in those cases where efficacy beliefs tended to be

weaker, the respondents indicated that they felt “uncertain” rather than openly negative about

their future skills.

In terms of learning knowledge necessary to be successful mathematics teachers, teacher

education students responded with strong efficacy to the statements “I will continually find better

ways to teach math” (M = 4.57, SD = .61) and “I will understand math concepts well enough to

be effective in teaching elementary math” (M = 4.36, SD = .65). They demonstrated the weakest

efficacy for an item that reflects their ability to inspire their students (“I will not know what to do


to turn students on to math” [reverse coded]; M = 3.79, SD = .72) rather than for mastery of

content, but again, their efficacy even on this item was quite high (“uncertain” to “agree”).

In addition, two self-efficacy scales (self-efficacy for student engagement, SESE, and

self-efficacy for instructional strategies, SEIS) from the TSES – short form (Tschannen-Moran &

Woolfolk Hoy, 2001) were used to gauge teacher education students’ efficacy for specific tasks

related to mathematics instruction. Teacher education students responded with similar levels of

confidence to all three self-efficacy for teaching scales (M = 77.77% across the three scales, SD

=1.24%). Only a very small difference exists between the highest (SEIS) and lowest (SETM)

scoring scales (h = .07).

TSES items ask respondents how much they will be able to do with regards to specific

classroom tasks. Items are rated from 1 (“Nothing”) to 9 (“A great deal”). On average, students

rated how much they would be able to do in terms of both instructional strategies and student

engagement as “Quite a bit” (SEIS: M = 7.16, SD = 1.34, SESE: M = 6.93, SD = 1.15). Two

student engagement items were rated less positively: “How much will you be able to do to

motivate students who show low interest in math schoolwork” (M = 6.79, SD = 1.31) and “How

much will you be able to do to assist families in helping their children do well in math?” (M =

6.68, SD = 1.59). The most positively rated item indicated teacher educations students had

relatively high levels of efficacy for depth of their understanding of the mathematics content:

“To what extent will you be able to provide an alternative explanation or example when students

are confused about math?” (M = 7.30, SD = 1.45).

Outcome Expectancies

Items drawn from the MTEBI (Enochs, Smith, & Huinker, 2000) and STEBI (Riggs &

Enochs, 1990), or created to be similar in format (Olson, 2014), were used to measure outcome


expectancies that framed the difficulty of making changes in student achievement with respect to

the role of teachers, students, and content. Similar to the MTEBI self-efficacy items, outcome

expectancy items were rated from a low score of 1 indicating participants “strongly disagree”

with the ability for students or teachers to make changes in student achievement to a high score

of 5 indicting participants “strongly agree” with the ability of students or teachers to make

changes in student achievement.

Teacher education students tended to respond more positively to the teacher scale

(71.37%) and student scale (65.09%) than to the content scale (56.53%). However, the

difference between student and content scales (h = .18) and the difference between teacher and

content scales (h = .31) were small effects.

Teacher items formed an internally consistent scale. Students tended to respond to these

items between “uncertain” and “agree”. For example, high agreement items included, “The

inadequacy of a student’s math background can be overcome by good teaching” (M = 3.92, SD

= .68) and “When the math grades of students improve, it is often due to their teacher having

found a more effective approach” (M = 3.87, SD = .76). A lower agreement item was “If

students are underachieving in math, it is most likely due to ineffective math teaching” [reverse

coded] (M = 3.13, SD = .96), suggesting that while teacher education students agreed that student

achievement was due to teachers’ influence, they were less likely to agree that student

underachievement was due to teachers’ influence.

The student and content items did not form internally consistent scales; however, from an

exploratory perspective, examining items allows further insight into teacher education students’

beliefs even if the scales are not consistent enough to use as full measures in the models. The

student belief items were all reverse coded, resulting in item averages ranging from “disagree” to


“agree” on the Likert scaling. Following reverse coding, a high agreement item was

“Effectiveness in math teaching has little influence on the achievement motivation of students

with low motivation” (M = 3.64, SD = .88). A low agreement (high disagreement) item was,

“The low math achievement of some students cannot be blamed on their teachers” (M = 2.77, SD

= .80). The scale’s low reliability may be due to teacher education students’ ambiguity of when

teachers or students are responsible for achievement. For example, in these items, teacher cannot

influence students with low motivation but they should also be held responsible for students’ low

achievement.

Given the purported mathematics anxiety of pre-service teachers, it seemed prudent to

include items that attempted to measure the degree to which the content area influences the

general ease or difficulty of making changes in student achievement. Thus, several items were

created to ascertain teacher education students’ general beliefs about math. Teacher education

students agreed that math requires more effort than other subjects [reverse coded] (M = 2.94, SD

= 1.10), math makes more sense than other subjects (M = 3.28, SD = .95), people worry more

about being successful in math than other subjects [reverse coded] (M = 2.11, SD = .82).

Teacher education students disagreed that math is more difficult than other subjects [reverse

coded] (M = 3.68, SD = .83) and that people like taking math more than other subjects (M = 2.11,

SD = .64).

Note that across the items drawn from the MTEBI and STEBI and used to form self-

efficacy to teach and learn mathematics (SETM, SELM) and outcome expectancy scales (OES,

OET), as well as the items in the outcome expectancies for mathematics scales intended to be

consistent with the other MTEBI and STEBI items, teacher education students responded with

the lowest levels of agreement to items that were phrased negatively and intended to be reverse


coded. Perhaps the negative framing of the items contributed to the low levels of agreement

beyond the intended measure of content and thus artificially lowered agreement. However, the

percent agreement with the self-efficacy scales drawn from these sources and those drawn from

the TSES are consistent, again suggesting the relatively high levels of self-efficacy in this group.

Model Analyses

The intention of future work is to evaluate models that relate mathematics anxiety, self-

efficacy, and (pre-service) teacher outcomes. However, the sample size in the current study is

not optimal for modeling approaches. Hence, traditional statistical analyses of observed

variables were used, as informed by Hayes (2013), Stevens (2009), and Tabachnick and Fidell

(2013). These include binary logistic regression, sequential multiple regression, analysis of

mediation, analysis of variance, and dependent-sample t-tests, in addition to the reporting of

descriptive statistics and effect size measures. All analyses were performed using SPSS

Statistics 20.0 and the PROCESS 2.11 macro created for SPSS by Hayes (2014).

Diagnostics: Tests of Assumptions

Absence of univariate outliers. Univariate outliers occur when cases have very large

standardized scores, resulting in departure from normality in the variable’s distribution. Outliers

affect the regression solution too greatly (i.e., pull the solution toward outlying values), and thus,

should be removed prior to regression analysis (Tabachnick & Fidell, 2013). Initial exploration

for outliers was conducted using SPSS EXPLORE to test skewness (sk), kurtosis (kur), and the

Kolmogorov-Smirnov (D) test of normality for all variables intended to be used in model

analysis, including the four self-efficacy variables (SELM, SEIS, SESE, SETM), the two

mathematics anxiety variables (MAL, MAT), the reliable outcome expectancy variable (OET),

as well as the two dependent variables (Grade Level Preference, Subject Area Preference).


These values are presented in Table 3. Tabachnick & Fidell (2013) suggest that skewness and

kurtosis beyond the criterion of z = 3.29 serve as indicators that a distribution has outliers. The

D test of normality is preferred to the Shapiro-Wilk test with small sample sizes, but like the

Shapiro-Wilk, it may be overly sensitive with extremely small samples like those in this study

(Tabachnick & Fidell, 2013). Thus, the combination of the three diagnostics was used to

evaluate potential violations of assumptions.

No egregious violations in normality were found in skew and kurtosis except on the

variable, SEIS (zsk = -3.83, zkur = 3.54, D = .15, p = .004), which exceeded the Tabachnick &

Fidell (2013) criteria. A box plot and histogram were used to further assess the departures from

normality and identify outliers in the SEIS as per the recommendations of Stevens (2009) and

Tabachnick & Fidell (2013). This resulted in removal of four outliers from analyses that used

the SEIS variable (Model 2). The students with outlying scores on this variable rated their self-

efficacy for instructional strategies as extremely low (SEIS < 20) in comparison to their peers,

but their responses on the other variables were not unusual for the sample.

Additionally, exploration of the variables indicated that the sample over-represents

teacher education students who hope to teach early elementary (n = 21; 39.6% of the total

sample) or upper elementary grades (n = 24; 45.3% of the total sample), while under-

representing teacher education students primarily interested in teaching middle school (n = 2;

3.8% of the total sample) or high school n = 6; 11.3% of the total sample). This resulted in

removal of participants preferring middle school and high school from the analyses using grade

level preference (Model 1).


Table 3

Exploration of Assumptions of Univariate Skewness, Kurtosis, and Normality

Scale sk zsk kur zkur D pD Self-Efficacy to Learn Mathematics Knowledge for Teaching (SELM)

-.65 -1.99 .54 .83 .15 .005

Self-Efficacy to Teach Mathematics (SETM)

.41 1.26 .03 .05 .11 .176

Self-Efficacy for Instructional Strategies in Mathematics (SEIS)

-1.25 -3.83 2.28 3.54 .15 .004

Self-Efficacy for Supporting Student Engagement in Mathematics (SESE)

-.28 -.86 -.60 .93 .11 .182

Mathematics Learning Anxiety (MAL) .47 1.44 -.90 -1.40 .14 .012 Mathematics Teaching Anxiety (MAT) .53 1.63 -.45 .70 .12 .049 Outcome Expectancies for Teachers in Mathematics (OET)

-.20 -.60 -.47 -.73 .08 .200

Grade Level Preference 1.14 3.47 .65 1.00 .29 < .001 Subject Area (Mathematics) Preference -.391 -1.18 -1.20 -.65 .23 < .001

Normality, linearity, and homoscedasticity of residuals. Regression assumes that the

prediction errors (residuals) are normally distributed around each predicted score and that the

relationship between the predicted scores and errors is linear. Homoscedasticity refers to the

distribution of residuals. The assumption states that residuals must be normally distributed as

opposed to non-normal or heteroscedastic distributions. Observation of the predicted scores

against residuals via P-P plots and the distribution of the standardized predicted scores against

standardized residuals via scatter plots was conducted following each regression run. Results

indicated no major violations of the assumptions of normality, linearity, and homoscedasticity.

Independence of errors. Further, regression analysis assumes that residuals are

independent of one another. When the independence assumption has been met, the Durbin and

Watson (1951) test should yield a diagnostic value around 2 (i.e., not less than 1 and not greater

than 3). Durbin-Watson test values are reported.


Multicollinearity. Multicollinearity among variables results in large standard errors of

regression coefficients, reducing power to detect significant predictors. Multicollinearity is

assessed using Tolerance and Variance Inflation Factor (VIF) diagnostics. Tolerance is

measured by subtracting R2 from one. VIF measures the correlation of each variable to the

others in the model, and thus is consistent with R2 and the reciprocal of Tolerance. When

diagnostics indicate that VIF is low (below 2) and Tolerance is high, the threat of

multicollinearity is minimized. However, when the assumption is violated, it becomes more

difficult to detect and interpret b coefficients. Thus it is important to set criteria for determining

when multicollinearity is a valid threat to findings. Historically, measures of Tolerance less than

or equal to .2 were used to indicate multicollinearity, but Tabachnick and Fidell (2013) suggest

that when Tolerance is as high as .5 or .6, multicollinearity may still be a threat. Thus, both VIF

and Tolerance are reported to serve as multiple diagnostics, and in this study, all observed VIF

values are below 1.5 and all Tolerance values are above .7, indicating little risk of

multicollinearity in the models.

Violation of regression assumptions relates to the power available to detect significance

of predictors and also to the accuracy of confidence intervals generated for the b coefficients

(rather than the estimation of the b coefficients). Significance tests and confidence intervals

should provide the same information about the utility of a predictor (i.e., a significant predictor

should not have zero in the confidence interval). However, this is not always the case. Where

minor violations of regression assumptions occur, bootstrapping can be used to generate more

accurate confidence intervals as is done in the Hayes (2014) procedure. Kirk (2008) suggests

that when confidence intervals indicate the utility of a predictor, it should remain in the model


even if statistical tests suggest that it is not significance. Given the robustness of the Hayes

(2014) confidence intervals, this decision rule was adopted for the following model analyses.

Model 1: Grade Level Preference

Based on the literature, it was hypothesized in the first model (Figure 4) that higher levels

of mathematics anxiety and more negative outcome expectancies associated with mathematical

content would lead to lower levels of self-efficacy, which in turn, would predict that teacher

education students’ preference for teaching earlier grade levels. However, the low level of

reliability associated with the mathematics outcome expectancies makes it inappropriate to

include these in testing the model. Thus, the revised hypothesis (depicted in Figure 6) suggests

that self-efficacy is a mediator in the relationship between anxiety for learning mathematics and

grade level preference. Further, the restriction of range in the grade level preference variable

resulted in revision of the analysis to test if anxiety (MAL) and self-efficacy around learning

mathematics content (SELM) significantly predicted teacher education students’ preference for

teaching early elementary (K-3) or upper elementary grades (4-5), N = 46.

Figure 6

Revised Model 1: Self-Efficacy for Learning Mathematics as a Mediator in the Relationship

between Anxiety for Learning Mathematics and Grade Level Preference

The PROCESS 2.11 macro developed by Hayes (2014) was used to estimate the direct

and indirect effects of mathematics learning anxiety (MAL) with the self-efficacy for learning


mathematics factor (SELM) as a mediating variable. Given the small sample size, this approach

has the advantage of using a single significance test for mediation (and thus increasing protection

from familywise alpha errors) as well as built-in bootstrapping methods to generate confidence

intervals for the indirect and mediated effects that makes the analysis more robust to potential

violations of assumption of normal distributions of scores. Further, it is appropriate to use with

the binary outcome, grade level preference.

In the binary logistic regression analysis, the dependent variable was grade level

preference, the independent variable was anxiety for learning mathematics, and the proposed

mediating variable was self-efficacy to learn mathematics. Table 4 reports the regression of

anxiety for learning mathematics and self-efficacy for learning mathematics on grade level

preference. Figure 7 reports the total, direct, and mediation effects. There was no support for

the hypothesis; a test of the full model with the predictor and hypothesized mediator against a

constant-only model was not statistically significant χ2(2, N = 45) = 2.787, p = 0.248. The

McFadden’s D effect size, an effect size measure appropriate to use with logistic regression, was

.04, and only 57.1% of early elementary and 70.8% of upper elementary teacher education

students were correctly classified. Thus, the anxiety and self-efficacy measures around learning

mathematics do not reliably distinguish between teacher education students interested in teaching

early elementary or upper elementary grades.


Table 4

Correlations and b Coefficients for Logistic Regression of Mathematics Learning Anxiety (MAL)

and Self-Efficacy for Learning Mathematics (SELM) as Predictors of Grade Level Preference

Zero-Order r Variable SELM MAL b p Bootstrap 95% CI Constant -.16 -.17 4.41 .134 [-1.36, 10.18] SELM -.10 -.04 .241 [-.10, .02] MAL -.02 .206 [.05, .01] Direct Effect -.02 [-.06, .01] Indirect Effect .00 [0, .02]

Figure 7

Non-Significant Predictors in the Relationship between Anxiety for Learning Mathematics, Self-

Efficacy for Learning Mathematics, and Grade Level Preference

Model 2: Subject Area Preference

Model 2 hypothesizes that teacher education students’ experience of self-efficacy for

teaching mathematics (SETM, SEIS, SESE) should predict their global preference for teaching

mathematics (as compared to other core subject areas). Self-efficacy theory further suggests that

experience (vicarious and mastery) and anxiety (physiological arousal) should predict self-


efficacy. In addition, the argument presented in this paper suggests that outcome expectancies

(general efficacies) should likewise influence self-efficacy, particularly for novices. Model 2

(Figure 8) thus predicts that self-efficacy for teaching mathematics (SETM, SEIS, SESE)

mediates the relationship between mathematics teaching anxiety (MAT), outcome expectancies

about teachers’ and students’ influence on students’ mathematics achievement (OE), vicarious

and mastery experiences (VE), and global preference for teaching mathematics (in comparison to

other core subject areas).

Figure 8

Revised Model 2: Relationship between Anxiety for Teaching Mathematics, Outcome

Expectancies for Teaching Mathematics, Self-Efficacies for Teaching Mathematics, and Subject

Area Preference for Mathematics

Model 2 questions include:

1. Do any of the measures of self-efficacy (SESE, SEIS, SETM) predict the outcome of

preference for teaching mathematics?


2. Do any of the factors (MAT, OE, VE, ME) theorized to predict self-efficacy do so?

3. Does self-efficacy mediate the relationship between predictive factors and the outcome?

Given the complexity of the model and the relatively low ratio of participants to predictors,

the model was first pruned of all non-significant predictors prior to evaluation of the potential

mediation effect. Thus, each of the three model questions was addressed independently.

However, to account for the potential for familywise alpha errors, each question was addressed

with a Bonferroni corrected alpha (α = 0.05/3 = 0.017).

As noted earlier, preliminary evaluation of assumptions indicated that four participants

were extreme outliers on the self-efficacy for instructional strategies variable (SEIS), leading to

non-normal distribution (zsk = -3.83, zkur = 3.54, D = 15, p = .004). These participants were

removed from analysis, resulting in a sample size of N = 48.

Model 2A hypothesizes that participants’ experience of self-efficacy for teaching

mathematics (SETM, SEIS, SESE) should predict their global preference for teaching

mathematics (as compared to other core subject areas). SPSS REGRESSION was run with

preference for mathematics as the dependent variable and the three self-efficacy for teaching

variables as independent variables (predictors). Table 5 displays the results of the regression

analyses for this question.

Exploration of residuals was undertaken. The Durbin-Watson test of independence of

errors was acceptable (DW = 1.77), and diagnostics for multicollinearity suggested a low level of

multicollinearity threat (SESE: Tolerance = .71, VIF = 1.40; SEIS: Tolerance = .71, VIF = 1.42;

SETM: Tolerance = .93, VIF = 1.07). Residuals were also examined with P-P plots, suggesting

little need to be concerned with the distribution of residuals. However, scatterplots indicated

some potential that residuals were associated with the categorical outcome variable.


Consistent with the hypothesis, R = .48, F(3, 45) = 4.49, p = .008, with R2 = .23, and 95%

CI [0.04, 0.42]. The adjusted R2 value of .18 indicates that a little less than one-fifth of the

variability in overall confidence is predicted by SETM, SEIS, and SESE. However, only the

regression coefficients for self-efficacy to teach mathematics (bSETM = 1.15, p = 0.001) differed

significantly from zero, 95% CI [.47, 1.83]. Self-efficacy for mathematics instructional

strategies (SEIS, p = 0.610) and self-efficacy for student engagement in mathematics (SESE, p =

0.869) did not significantly contribute to students’ preference for teaching mathematics.

Table 5

Correlations and b Coefficients for Standard Multiple Regression of Self-Efficacy for Teaching

Variables (SESE, SEIS, SETM) on Subject Area Preference for Mathematics

Zero-Order r Model Variable SESE SEIS SETM b p 95% CI

2A

Math Preference .12 .18 .48* -33.83 .361 [-107.67, 40.01] SESE .53* .22 -.06 .869 [-.84, .71] SEIS .24 .22 .610 [-.64, .1.08] SETM 1.15 .001 [.47, 1.83]

2B Constant -20.82 .338 [-64.08, 22.45] SETM 1.15 < .001 [.60, 1.71]

* p < .001

The SESE and SEIS variables were removed; neither their b coefficients nor their CIs

suggested keeping them in the model. The participants who had scored as outliers on SEIS were

returned to the sample given that they were not outliers with respect to their responses on the

SETM variable, resulting in N = 52.

The revised model resulted in R = .51, F(1, 50) = 17.54, p < 0.001, with R2 = 0.26, 95%

CI [.06, .46]. Adjusted R2 = .25, indicating that approximately one quarter of the variability in

subject area preference is predicted by the single self-efficacy variable, SETM. With only one


predictor in the model, there was no need to review collinearity diagnostics. The diagnostic for

independence of errors was again acceptable (DW = 1.94) as was the P-P plot of the residuals.

For the second question, self-efficacy theory suggests that experience (vicarious and

mastery) and anxiety (physiological arousal) should predict self-efficacy. Further, the argument

presented in this paper suggests that outcome expectancies (general efficacies) should likewise

influence self-efficacy, particularly for novices. Thus, an SPSS REGRESSION model was run

to explore whether experience (ME, VE), mathematics teaching anxiety (MAT), and outcome

expectancies (OET) predicted the SETM variable (Model 2C). Regression results are reported in

Table 6.

Table 6

Correlations and b Coefficients for Standard Multiple Regression of Experience (ME, VE),

Mathematics Teaching Anxiety (MAT), and Outcome Expectancies for Teachers (OET) on Self-

Efficacy for Teaching Mathematics (SETM)

Zero-Order r Model Variable VE ME OET MAT b p 95% CI

2C

SETM .39** .10 -.49*** -.28* 102.71 < .001 [76.28, 129.14] VE .37** -.12 -.09 .14 .007 [.04, .23] ME -.11 -.26* -.05 .317 [-.16, .05] MAT .13 -.33 < .001 [-.51, -.16]

OET -.25 .134 [-.57, .08]

2D SETM 87.50 < .001 [76.95, 98.05] VE .13 .005 [.04, .22] MAT -.34 < .001 [-.51, -.16]

2E

Math Preference SETM MAT VE

21.93 .83 -.44 .05

.479

.013

.059

.658

[-39.80, 83.65] [.18, 1.49] [-.89, .02] [-.18, .28]

Indirect of MAT .27 [-.64, -.08] Indirect of VE .10 [.02, .25] * p < .05, ** p < .01, *** p < .001.


Analysis of residuals indicated no major concerns. The Durbin-Watson test of

independence of errors was acceptable (DW = 1.95), and diagnostics for multicollinearity

suggested a low level of multicollinearity (VE: Tolerance = .85, VIF = 1.18; ME: Tolerance =

.83, VIF = 1.21; MAT: Tolerance = .97, VIF = 1.02, OET: Tolerance = .91, VIF = 1.10).

Residuals were also examined with P-P plots and scatter plots, suggesting no need to be

concerned with the distribution of residuals.

Consistent with the predicted relationships, R = .62, F(4, 48) = 7.45, p < .001, with R2 =

0.33, and 95% CI [.14, .52]. The adjusted R2 value of .33 indicates that one-third of the

variability in overall self-efficacy for teaching mathematics is predicted by the combination of

anxiety, vicarious experience, outcome expectancy, and mastery experience variables.

Regression coefficients for anxiety (bMAT = -.33, p < .001, 95% CI [-.51, -.16]) and vicarious

experience (bVE = .14, p = .007, CI 95% [.04, .23]) differed significantly from zero.

The non-significant predictors were removed and the model was re-run, resulting in R =

0.59, F(2, 50) = 13.24, p < 0.001, with R2 = 0.35, and 95% CI [0.15, 0.55]. The adjusted R2

value indicated that 32% of the variability in subject preference is predicted by the combination

of anxiety for teaching mathematics and anxiety for vicarious experience. bMAT = -.34, p < .001,

with 95% CI [-.51, -0.16], and bVE = 0.13, p = 0.005, with 95% CI [.04, .22].

Following the revision of the model, residuals were again examined. The Durbin-Watson

test of independence of errors was acceptable (DW = 1.84), and diagnostics for multicollinearity

suggested a low level of multicollinearity (Tolerance = .99, VIF = 1.02). Residuals were also

examined with P-P plots and scatter plots, suggesting no need to be concerned with the

distribution of residuals.


Finally, the mediation effect (Model 2E) was tested using PROCESS 2.11. In order to

test two independent variables (MAT, VE), Hayes (2013) recommends that PROCESS 2.11 be

run twice, each time with one of the independent variables as the predictor and the other as a

covariate. Although this does not allow for a single test of the total indirect effect across all

independent variables, it does afford estimates and tests for each independent variable.

Figure 9

Significant Predictors in the Relationship between Vicarious Experience, Mathematics Teaching

Anxiety, Self-Efficacy for Teaching Mathematics, and Subject Area Preference for Mathematics

In the first run, the dependent variable, subject area preference, was predicted from

mathematics teaching anxiety (MAT), vicarious experiences (VE) were treated as a covariate,

and the self-efficacy measure (SETM) was treated as a potential mediator. In the second run, the

dependent variable, subject area preference, was predicted from vicarious experience (VE),

mathematics teaching anxiety (MAT) was treated as a covariate, and the self-efficacy measure

(SETM) was treated as a potential mediator. Model 2E was significant; R = .55, F(3, 48) = 7.33,

p < .001, with R2 = .31, and CI 95% [.12, .50]. Unstandardized coefficients for all significant

paths in this model appear in Figure 9 and measures of total, direct, and mediation effects appear

in Table 6. Results indicate that the anxiety (b = -.33, p = .001) and vicarious experience (b =


.12, p = .017) significantly predict self-efficacy, self-efficacy significantly predicts subject area

preference (b = .83, p = .013), but anxiety (b = -.44, p = 0.059) and vicarious experience (b = .05,

p = 0.658) do not significantly predict the outcome with the mediator in the model. Thus, self-

efficacy appears to mediate the relationship between anxiety, vicarious experience, and subject

area preference. The indirect effect of mathematics teaching anxiety on subject area preference

is -.27 (Boot 95% CI [-.64, -.08]), and the indirect effect of vicarious experience on subject area

preference through self-efficacy is .10 (Boot 95% CI [.02, .25]). The bootstrap samples for bias

corrected confidence intervals included 1000 samples.

Analysis of Learning Block Participation

Selection into Learning Block Participation An exploratory analysis of variance was run to determine if there were any variables of

interest that could help explain which teacher education students selected into participation in the

learning blocks. Given the small sample size of students who elected to complete the learning

blocks and concomitant lack of power, Cohen’s d (Cohen, 1988) is reported in addition to

significance levels. Surprisingly, there were no significant differences between the 22 teacher

education students who chose to complete and the 30 teacher education students who chose not

to complete the learning blocks on any of the variables in this study: anxiety to teach (p = 0.647,

d = .13) or learn math (p = 0.644, d = .13), mastery (p = 0.725, d = .10) or vicarious experiences

(p = 0.962, d = .01), self-efficacy to teach (p = 0.199, d = .36) or learn math (p = 0.346, d = .27),

preference for teaching mathematics as a core subject (p = 0.557, d = .17), or preferred grade

level to teach (p = 0.554, d = .17). Thus, there were small effect size differences between the

groups on self-efficacy to teach mathematics, and self-efficacy to learn mathematics. As would


be expected from theory, in both cases the teacher education students with higher self-efficacy

chose to participate in the learning blocks.

Experience with Learning Blocks The analyses presented above suggest that mathematics teaching anxiety (MAT) and self-

efficacy for teaching mathematics (SETM) hold promise for explaining teacher education

students’ attitudes toward their professional work as mathematics teachers. Additionally, self-

efficacy for learning mathematics (SELM) may also contribute to teacher education students’

willingness to participate in educational experiences before they enter the classroom. Finally,

although outcome expectancy dropped from the model, the initial hypothesis was that outcome

expectancies could be influenced via social persuasion, which in addition to the vicarious

experience of watching expert teachers provided in the learning blocks, may be an effect of the

professional development materials. It was therefore important to consider whether experiences

with the professional development materials were able to make changes in any of these variables.

Dependent t tests were conducted to determine if change occurred in any of these variables.

Given the small sample size, d is again reported in addition statistical significance in Table 7.

Table 7

Mean Differences from Time 1 to Time 2 in Self-Efficacy, Mathematics Anxiety, and Outcome

Expectancy Variables with Participation in Learning Blocks

Variable MD SDD p d Self-Efficacy to Teach Mathematics (SETM) -1.36 6.58 .342 -.27 Self-Efficacy to Learn Mathematics (SELM) .91 7.66 .584 .16 Mathematics Teaching Anxiety (MAT) -3.06 12.87 .278 -.32 Outcome Expectancies for Teachers (OET) 1.82 9.92 .399 .24


Results indicated that participating teacher education students did not make significant gains

with participation in the learning blocks; however, effect size measures suggest several

interesting findings to consider in future work. In terms of self-efficacy, participating teachers

felt more efficacious in learning mathematics knowledge necessary to be successful teachers (d =

.16), but the experience made them less confident in their ability to teach (d = .27). The largest

effect was for reducing anxiety for teaching mathematics (d = .32). Outcome expectancies did

show a small effect (d = .24) for increasing in positivity of beliefs that teachers in general can be

successful in making changes to student achievement outcomes.

Response to Learning Blocks Teacher education students reviewed two learning blocks that were also reviewed by

Noyce teachers. Table 8 depicts the results of general feedback survey questions for both

groups. In general, both groups responded extremely positively to the learning blocks, judging

them to be useful for in-service teachers with experience, new teachers, and pre-service teachers.

However, both groups rated the materials as most useful to new teachers.

In terms of the content, both groups felt that the Key Ideas learning block focused on

review of material that was available to them in other places. Likewise, both groups felt that the

Absolute and Relative Thinking learning block was a combination of new and review material,

perhaps indicating that it builds on previously-learned content. Unsurprisingly, the Noyce

teachers, who have many opportunities to participate in mathematics-focused professional

development, were more likely to rate the materials as overlapping other professional

development experiences they have had. For the teacher education students, this experience was

wholly new.


Table 8

Mean, Standard Deviation, and Mode of Teacher Education Student and In-Service Teacher

Responses to Learning Blocks

Feedback Absolute and

Relative Thinking Key Ideas

Students Teachers Students Teachers

Overall M (SD) Mode

3.95 (.90) Useful

4.5 (.5) Very

4.11 (.74) Useful

3.67 (.47) Useful

In-Service M (SD) Mode

3.85 (.89) Useful

4 (0) Useful

4.26 (.71) Very

4 (.82) Useful

New Teachers

M (SD) Mode

4.5 (.58) Very

4.5 (.5) Very

4.58 (.59) Very

5 (0) Very

Pre-Service M (SD) Mode

4.45 (.72) Very

4 (1) Useful

4.53 (.60) Very

4.67 (.47) Very

Newness M (SD) Mode

2 (.44) Combination

1.5 (.5) Combination

1.42 (.59) Review

1 (0) Review

Overlap M (SD) Mode

1.85 (1.08) No

2.5 (.5) Some

2.11 (1.33) No

2.67 (1.25) Some

Another goal of this work was to investigate whether teacher education students would

request different additional materials, clarifications, or improvements than previously studied in-

service teachers when reviewing the learning blocks. Teacher education students, Noyce

teachers, and a larger group of in-service teachers not associated with the Noyce program

provided qualitative feedback after reviewing the two learning blocks. As can be seen in Table

9, students and teachers shared many of the same themes in their feedback. For example, both

groups particularly liked many of the same aspects of the learning blocks, including example

videos of teacher-student interactions, example problems and activities that could be readily


incorporated in ongoing instruction or lesson planning, and clarity of explanations of terms (e.g.,

“absolute” and “relative”).

The feedback indicated that teachers and students were able to distinguish the major

objectives of each block, and their responses further indicated that they will use this content in

the current or future classrooms. For example, a major objective of the Absolute and Relative

Reasoning learning block was to help clarify the distinction between absolute and relative

reasoning, and provide support for teachers to use more relative reasoning in their classrooms.

Responses indicated that both groups intended to engage students in relative reasoning, create

new questions to elicit relative reasoning, adapt their existing materials to incorporate more

opportunities for students to engage in relative reasoning, and be more aware of the questions

they write and whether they support absolute, relative, or both types of student thinking.

Similarly, the two goals of the Key Ideas learning block were to help support the use of multiple

representations of rational numbers in the classroom and to help teachers better utilize practice

around these difficult concepts. Both groups indicated strategies they would use to incorporate

the key ideas and improve their practice activities.

In some cases, there were no responses that were unique to either the teacher education

students or the in-service teachers. For example, teachers did not identify unique strengths in the

Absolute and Relative Reasoning learning block. Similarly, students did not identify unique

implications for practice in the Key Ideas learning block. Further, the groups identified all the

same strengths in the Key Ideas block (i.e., videos, activities, examples).


Table 9

Learning Block Feedback: Major Themes and Responses from In-Service Teachers and Teacher

Education Students

Learning Block

Themes Group Responses

Absolute and Relative Reasoning

Helpful ideas to put into practice

Both groups

• Engage student in relative reasoning. • Create new relative questions. • Adapt existing questions to be more

relative. • Model multiple ways to solve problems. • Make connections to specific content not

covered in block (e.g., rates, negative numbers).

• Make connections to real world content; personalize content for student interests.

• Be more aware of how problems are framed and the kinds of thinking they will generate.

Teachers

• Identify students as particular types of thinkers (relative versus absolute).

• Explain the difference between absolute and relative thinking to students.

Students • Connect to research about importance of relative thinking.

Requests for revision of material

Both groups

• Provide additional problems, activities, and resources that use relative thinking.

• Demonstrate how “relative” thinking connects to higher-order thinking skills/upper levels of Bloom’s taxonomy.

Teachers • Provide “quick” ways to engage student thinking without using much class time.

Students

• Explain how block content relates to grade-level expectations.

• Connect content to Common Core State Standards, especially fraction standards.

• Connect to other core subjects. • Make the experience more interactive. • Improve the “cactus” problem.

Favorite or strongest parts of learning block

Both groups

• Demonstrations of problems set in real-world contexts

• Example videos


experience • Clarity of explanations of “relative” and “absolute”

Teachers no unique responses

Students • Embedded learning checkpoints • Overall organization and objectives

Key Ideas

Helpful ideas to put into practice

Both groups

• Introduce concept of “renaming” numbers. • Focus on identifying whole/unit. • Help students become accustomed to

multiple representations. Connect representations across rational number forms. Ask students to report answers in multiple forms.

• Use more visual representations in teaching.

• Personalize example problems/incorporate real world examples.

• Teach estimation and how to check for meaningfulness.

• Ask students to create their own problems. • Ask students to explain their reasoning to

the teacher and to each other. • Provide opportunities for in-class practice

(rather than homework). Use this time to provide immediate feedback.

• Be careful to distribute practice. Make sure students have adequate time for practice. Be aware that the individual needs students have for practice will vary.

• Provide students with meaningful feedback (relevant to observable criteria and common errors).

Teachers

• Teach students to ask questions and seek clarification.

• Accept multiple solutions as correct. • Minimize homework assignments and

grading. • Incentivize homework. • Practice being clear and explicit in

explaining concepts. Students no unique responses

Requests for revision of material

Both groups

no overlap in responses

Teachers • Provide interactive websites where students can explore multiple


representations of numbers. • Clarify order in which key ideas should be

taught.

Students

• Provide more examples of real-world fraction use (not pizzas or pies).

• Provide “best language” for explaining key ideas to students.

• Provide more support for teaching place value.

• Provide examples of meaningful feedback. • Provide ideas for motivating students to

engage in practice. • Connect to Common Core State Standards. • Include more visuals and interactivity in

the learning block. • Subtitle videos.

Favorite or strongest parts of learning block experience

Both groups

• Example videos • Example activities (e.g., renaming, place

value) • Example questions to ask students

Teachers no unique response Students no unique responses

In contrast, there were no overlapping comments in the requests for revision for the Key

Ideas learning block. Teachers’ responses focused on the activities they would use as part of

their instruction around the key ideas. They requested additional support via interactive websites

and more help in organizing order and sequence of concepts. In contrast, students’ responses

focused on increased need for structure and examples of how to do the suggested practice (e.g.,

more detail on how to provide meaningful feedback, specific language to use when engaging in

instruction on key ideas, more about how to teach place value).

Some of the differences in response patterns came from teachers and students have

differing needs in the immediate future. For example, students were more often concerned about

broader issues of adapting the material to a variety of grade levels and types of learners.

Teachers, in contrast, were better able to connect the suggestions to specific content they needed


to teach (e.g., fractions, decimals, percents, negative numbers, number lines. Unsurprisingly

given the needs of each group, students were more likely to respond that they would use the

materials presented in the learning blocks to create lesson plans while teachers were more

focused on activities they could immediately use in their classrooms.

One unexpected difference in the responses was that students were more concerned about

bridging the learning block content to the Common Core State Standards. The in-service

teachers were more likely to want support in connecting the content to more general

organizational systems, such as Bloom’s Taxonomy and the related Higher-Order Thinking

Skills (HOTS).

Another unexpected difference in the responses was related to the Key Ideas material on

providing review opportunities for students. Both groups indicated that they had learned about

the need to provide meaningful and timely feedback to students and to provide time in class for

students to review so that teachers can detect misconceptions and common errors quickly “in the

moment” of the lesson. Thus, the major objectives were met for both groups. However, in-

service teachers also provided feedback that indicated they interpreted the review section as

suggesting that they minimize review problems, incentivize review and homework, and

minimize their grading of review problems (i.e., by grading only a few of the assigned items,

grading as a whole class, or having peers grade or provide feedback). It is interesting, and

somewhat discouraging, that in-service teachers interpreted the ideas presented about being

thoughtful in assigning review and practice such that students receive adequate practice without

review becoming “busy work” to mean they should minimize the review work both for students

and for themselves.


There were a few aberrant negative comments (e.g., a teacher disliked the idea of using

multiple representations and thought it would be confusing for her students, a student disliked

the “cactus” problem and felt that the ambiguity intended to provide opportunities for students to

explain their reasoning was not worth the confusion students experienced), but overall, the

responses to the learning blocks were exceptionally positive for both groups. For example,

students wrote final comments that indicated how useful the experience of in-service

professional development was for them while still in their teacher education programs. One

student commented, “This was very helpful! I especially thought the video of how to model

these problems was helpful to see students’ thinking.” Another wrote, “The explanations were

very clear, and I appreciated the practice problems throughout the slides in order to see how

these concepts could actually be used in classrooms.” In general, feedback indicated that the

utility of the blocks for students was in seeing how teachers incorporated content in real

classrooms.

Teacher responses were also quite positive. Teachers indicated that the learning blocks

were not only helpful, but made them think about their practice. For example, one teacher wrote,

“The more I thought about relative thinking, the more I realized that by doing problems like

these, that we are asking students to depend upon their prior knowledge in order to figure out the

answer. They are having to combine multiple math skills which keeps the math concepts fresh in

their minds and they are showing that they really understand the concept by apply it in out of the

box ways.” This theme of thinking through content in new ways was evident in other teacher

responses, such as “Great module. I never really took time to dissect these two concepts,” and “I

really liked this block! It sort of ‘clicked’ in my mind and helped me to think on how to teach

more ‘rationally’”. Thus, the utility of the experience differs slightly by group (i.e., opportunity


to observe how concepts can be implemented in classrooms versus opportunity to think more

deeply about content), but both groups found the materials helpful.


CHAPTER 5: DISCUSSION

Summary of Findings

Self-Efficacy

Based on the literature, it was hypothesized that teacher educations students would

respond with relatively low levels of self-efficacy for teaching mathematics as has been

demonstrated in multiple samples of pre-service teachers (Bursal & Paznokas, 2006; Gresham,

2008; Swars, Daane, & Giesen, 2006; Tooke & Lindstrom, 1998; Vinson, 2001). For example,

Bursal and Paznokas (2006) and Swars, Daane, and Giesen (2006) both found that pre-service

teachers responded with efficacy to 75% of the MTEBI items. The teacher education students in

this study indicated that they felt more confident than was expected about their abilities not only

to learn the content necessary to teach mathematics in elementary school classrooms (80%), but

that they also felt confident about their abilities to teach (77%), use appropriate instructional

strategies (80%), and even engage their students in the content (77%).

Perhaps unsurprisingly, the students in this sample felt more efficacious about their

ability to learn the content than to teach the content. Further, these students indicated strong

agreement that by the time they left the program, they would understand the mathematical

concepts well enough to be “effective” teachers. It is especially encouraging that students

indicated strong positive responses to items that assessed whether they saw themselves as

continuing to learn once they leave the program and enter the profession. For example, “I will

continually find better ways to teach math” was one of the items that students agreed with most

strongly. These findings indicate that students not only feel that their methods classes are


preparing them with adequate content knowledge, but that they understand that they will need to

continue to learn when they enter the profession.

While their efficacy scores were lower on items measuring teaching, the students seemed

at worst “uncertain” of their abilities in the classroom. This supposition is supported by the

lower ratings students gave items that ask about their certainty that they “have the skills

necessary to teach math” and the relative skill they have with have in mathematics as compared

to other core subject areas. Given the relatively low level of real classroom experience these

students have, uncertainty is probably a healthy response and is certainly consistent with self-

efficacy theory, which asserts that the self-efficacy of novices remains fluid until such time as

individuals have had successful (or unsuccessful) mastery experiences upon which to base their

forward-looking judgments.

One content area in which students were less certain that they would be able to learn

what they need to know to be successful teachers is how to inspire students in mathematics.

Both the item in the self-efficacy to learn mathematics content and two of the four items in the

self-efficacy for student engagement scales were rated with relatively low efficacy. In particular,

teacher education students reported lower self-efficacy for helping their students become

interested in mathematics, motivating them when they lost interest, and helping build

connections with families to improve student achievement in mathematics. Clearly, students

need more support to develop skills and confidence in teacher-student and teacher-family

relationships, particularly as these relate to motivating and inspiring students to remain involved

in mathematics.


Mathematics Anxiety

It was hypothesized based on the literature that teacher education students would

experience high levels of mathematics anxiety. Their responses did not indicate an extremely

high level of anxiety (i.e., they scored slightly below 50% anxiety on both scales). However,

these findings still indicate that about half of the time, these students feel measurable anxiety

(i.e., between “a little” and “a fair amount”) when they come into contact with mathematics

generally or are asked to engage in mathematics teaching. These findings suggest that these

students are actually equally or more anxious than other populations of pre-service teachers that

have been evaluated. For example, while some researchers have reported similar anxiety ratings

with this population (e.g., Bursal & Paznokas, 2006; Gresham, 2008), Hadley and Dorward

(2011) found that only 36% anxiety score on the same mathematics teaching anxiety used in this

study and researchers using more general measures of anxiety have found pre-service teachers to

respond with anxiety to as low as 38% of the scale (Swars, Daane, & Giesen, 2006). Further, the

students in this study are approximately equally anxious in learning and teaching. This suggests

an opportunity still exists to improve their experience of mathematics anxiety.

Further, improvement in mathematics anxiety may well be possible with experience in

the teacher education program. Both the learning (r = -.47, p = .010) and teaching (r = -.47, p =

.010) anxiety scales were significantly negatively correlated with years in the program. Thus,

the higher ratings of anxiety found in this study may be due to the relatively younger population

of students in the sample. Although the data are cross-sectional, and thus not causal, these

findings also suggest the potential to reduce mathematics anxiety across teacher education

coursework. Future research should investigate this potential longitudinally as well as attempt to

determine what aspects of the program experience best impact anxiety. The lack of relationship


between anxiety and measures of vicarious and mastery experience suggests that observation and

opportunity to practice skills are not the most important experiences for reducing anxiety.

A clear finding is that teacher education students felt the highest levels of anxiety in

evaluation settings. These included both evaluations of their own mathematics teaching and

learning (e.g., observation by an administrator, taking a math test) and evaluation of their future

students (e.g., preparing students for year-end tests and waiting for the results of their students’

year-end tests).


As expected teacher education students held more positive expectations related to

teachers (71%) and students (65%) than they did about the mathematical content (57%).

Students felt positive about the general ability of teachers to impact student achievement and also

believed teachers should take responsibility when students are not achieving, which is

encouraging given their professional plans. However, it was hypothesized that expectations shift

with social messages they receive in the program, and hoped that those messages become more

positive within a program than they may be in other venues. In contrast, no significant

relationships were found between the teaching outcome expectancy variable and experience in

the programs.

Model 1

The first model attempted to predict grade-level preference from mathematics anxiety

and self-efficacy for learning mathematics. Based on the literature, it was expected that higher

levels of mathematics anxiety would negatively impact pre-service teachers’ experience of self-

efficacy for learning the content and pedagogical content knowledge necessary to teach

mathematics effectively, which would in turn result in preference for teaching earlier grade


levels in which the mathematics content was perceived to be less difficult to master. However,

there was no support for this hypothesis. It is possible that the lack of support comes in part

from the restricted range of grades students wanted to teach in this study (primarily early and

upper elementary grades, with few students interested in teaching middle school or high school).

However, it is also possible that the constructs of mathematics anxiety and self-efficacy better

predict selection into the education field as a whole rather than to particular grade levels (i.e.,

that experiences of high mathematics anxiety and low self-efficacy predict choice of majors that

require fewer or lower level mathematics courses). This is consistent with Hembree’s (1990)

analysis and assertions made by Beilock et al. (2010). Future work should more closely examine

this possibility by modeling the relationship between mathematics anxiety, self-efficacy for

learning mathematics, and major choice.

Model 2

In analysis of Model 2, there was support for the relationship between vicarious

experience, mathematics teaching anxiety, self-efficacy for teaching mathematics, and preference

for teaching mathematics. Outcome expectancies failed to predict self-efficacy and preference,

causing them to be removed from the model. Further, given the low level of mastery experiences

in this group of novice teacher education students, it is not surprising that mastery experience

failed to predict self-efficacy or preference. However, these findings lend support to the

argument that in the absence of mastery experience, the other developmental pathways for

efficacy beliefs become more predictive of outcomes.

As expected from theory, self-efficacy beliefs were a strong predictor of mathematics

subject area preference. Further, the physiological arousal pathway (anxiety for teaching

mathematics) was a stronger predictor of self-efficacy than the vicarious experience pathway.


Thus, it may be especially useful to explore reducing anxiety in order to improve the self-

efficacy of low efficacy students before they enter the field.

Experience with Professional Development

Consistent with expectations from theory, there were small effect size (though non-

significant) differences between students who chose to complete learning blocks and those who

did not in terms of both self-efficacy for teaching and self-efficacy for learning content. If these

effects are replicated with a larger sample, they will provide support for the idea that task choice

(i.e., participation in professional development) can be predicted from experiences of self-

efficacy.

Experience with the learning blocks did not result in significant pre to post changes in

measures of anxiety, self-efficacy, or outcome expectancies. It is possible that the small sample

did not allow the power to fully investigate these effects. It is also possible that the dosage of the

learning block treatment simply was not great enough to elicit large effects. However, small,

non-significant effects were detected for both reducing mathematics teaching anxiety and self-

efficacy for teaching mathematics and increasing teacher outcome expectancies. Future work

should attempt to replicate these effects with a larger sample and/or more exposure to learning

blocks. If they are replicated, evidence will exist that professional development intended for in-

service teachers has the potential to reduce mathematics anxiety and increase teacher outcome

expectancies for teacher education students while they are still in their education programs.

The potential to reduce self-efficacy is interesting and unexpected. Given the relatively

high levels of self-efficacy exhibited by the students in this study, it is possible that students have

unrealistically high efficacy beliefs at this point in their careers. Bandura (1997) cautions against

unrealistic beliefs in that they can set the individual up for frustration when actual experiences do


not match beliefs. If their beliefs are unrealistically high, it is possible that future mastery and

vicarious experiences will initially lower self-efficacy for these students. If this is the case,

vicarious experiences and social persuasion embedded in professional development like that

presented in this study may help lower efficacy to more realistic levels without exposing students

to potentially damaging failure experiences. Moreover, access to experience like this when

students are still in a teacher education program provides a “safe” environment to participate in

new experiences.

Further, the results of learning block feedback indicate that the materials are appropriate

for pre-service as well as in-service teachers. Students indicated that they understood the same

key objectives as in-service teachers and both groups indicated they would utilize those

objectives in their (future) classrooms. Where the two groups differed tended to be in the lack of

experience that teacher education students have. Students wanted additional structure and

specific ways of teaching material to their students (even including specific language to

introduce concepts or use when providing feedback), whereas in-service teachers were more

comfortable with the instructional aspects and wanted instead additional activities to support

their instruction. Additionally structuring of examples may be necessary to fully meet the needs

of a pre-service population.

Interestingly, teacher education students were more critical of the online nature of the

learning blocks than in-service teachers. They were more likely to indicate that the learning

blocks were not interactive enough and to suggest technical fixes for problems (e.g., captioning

video to make student talk clearer to the listener). It is possible that students have more

experience with online learning and thus, are more critical of the products created by the Algebra

Ready team. In contrast, given that these students have little experience with teacher


professional development, it is also possible that they do not have an adequate sample of typical

professional development with which to compare Algebra Ready content, resulting in less

positive estimations than teachers with a good deal of experience with the types of professional

development regularly available in the field. Regardless of the source of the difference between

in-service teachers and teacher education students, these findings indicate that a greater level of

interaction may be needed to engage students in pre-service programs.

Another interesting difference between teacher education students and in-service teachers

was that the students were also much more concerned about the relationship between concepts

presented in the blocks and the Common Core State Standards. Several explanations could

account for this difference. Teachers in this state may not have fully implemented Common

Core; despite the state timelines for full implementation, Common Core assessment is only being

piloted this year and thus teachers’ evaluation may depend more on past sets of standards. In-

service teachers may also have had sufficient Common Core professional development through

other opportunities provided by their districts and the state. It is also possible there is more

pushback against the new standards in the schools than there is in the teacher education program.

Clearly, students in the program are aware of the new standards and concerned with matching

their content learning to the expectations outlined in the Common Core.

Overall, both the in-service teachers and teacher-education students were strongly

supportive of the utility of the materials for both pre-service and in-service professional

development. Both groups commented that the conceptual content made them consider aspects

of the mathematical content standards and their instruction that they had not previously

considered and that they felt the materials would improve their instruction. These findings are

similar to feedback received from previous iterations of the project (Good et al., 2013) and given


that four iterations of teachers (and now students) have responded positively to the blocks, there

is a good deal of support for their continued use.

Theoretical Implications

Self-Efficacy Theory

It was argued in this paper that self-efficacy can be predicted from mastery experience,

vicarious experience, social persuasion via the social transmission of outcome expectancies, and

physiological arousal via mathematics teaching anxiety. Further, it was argued that vicarious

experience, social persuasion, and physiological arousal would have greater impacts on the

development of self-efficacy for novices such as the teacher education students in this study. As

expected, students had relatively few mastery experiences and indeed mastery experience was

removed from the models predicting self-efficacy. There was support for the role of vicarious

experiences and anxiety in forming students’ self-efficacy. However, there was little support for

the argument that teacher outcome expectancies contribute to self-efficacy, and in fact, these

were removed from the model as well. Future work should investigate other forms of social

persuasion that students receive in their programs as well as how social persuasion relates to

collective efficacy of high- and low-performing schools and related shifts in outcome

expectancies when teachers enter the field.

Further, the modeling hypotheses indicated that not only did vicarious experience and

mathematics teaching anxiety predict students’ self-efficacy, but that their effect on the outcome

was perfectly mediated by the self-efficacy measure (i.e., the relationship between vicarious

experience, mathematics teaching anxiety, and the outcome ceased to be significant when the

mediating variable was entered in the model). This finding lends strong support to the causal

model theorized in self-efficacy approaches, as well as helps further explain the development of

self-efficacy for novices (i.e., prior to mastery experience).


Additionally, evidence from this study supports the assertion that self-efficacy predicts

task choice (both willingness to participate in professional development and preference for

teaching mathematics). It is not evident from this study whether the predictive nature of self-

efficacy functions similarly in actual teaching behavior and resilience to setbacks in the

classroom, although the evidence from the literature indicates this is likely the case (Friedman,

2000; Skaalvik & Skaalvik, 2007). Given these sources of evidence, self-efficacy appears to be a

useful point of intervention in order to ensure both good learning experiences in teacher

education programs and positive teaching behaviors as students transition to the profession.

Mathematics Anxiety Construct

Measures of mathematics anxiety indicated that students in the teacher education

program have more anxiety than would be expected from the results of other samples of pre-

service teachers in the literature. Mastery experience and vicarious experience were not related

to anxiety, but the length of time the student had been in the teacher education program was.

This suggests the potential importance of coursework to ameliorating anxiety in a population

expected to be highly anxious. Similarly, there were also indications that experiences with

professional development could also reduce anxiety for teacher education students. Thus, it is

important that future research investigate the characteristics of coursework and professional

development experiences that most positively impact anxiety.

The mathematics anxiety findings indicate strong anxiety for evaluation and weaker

anxiety for all other indicators. The evaluative component is not present in all situations in

which individuals engage in mathematics, but it is highly relevant to the research about how

mathematics anxiety develops. Studies suggest that students develop anxiety when they feel

humiliated or exceptionally concerned about failure and when they are provided with feedback


that the failure is unexpected, as in for example, experiences with teachers who did not

understand why they weren’t “getting it” (Brady & Bowd, 2005; Brown, McNamara, Hanley, &

Jones, 1999; Jackson & Leffingwell, 1999; Stoehr, Carter, & Sugimoto, 2013; Trujillo &

Hadfield, 1999; Uusimaki & Nason, 2004). It seems that it is not the mathematics that makes

people anxious, but rather the fear of failing, particularly failing in front of valued peers and

teachers. This has strong implications for how teachers are trained to interact with students, and

how to manage their own frustration when students have difficulty despite teachers’ best efforts.

Further, the findings also indicate a need to develop teachers’ depth of understanding so that they

have improved flexibility in how they explain content to students and greater understanding of

the potential misconceptions and indicators that suggest that the teacher’s instruction is not

effective.

Practical Implications

Self-Efficacy

Despite the use of scales designed by different authors, students scored similarly on all

three self-efficacy for teaching scales, thus, providing some evidence of the construct validity of

these scales (i.e., that all three scales measure the same construct). Unlike the items drawn from

the Mathematics Teacher Efficacy and Belief Instrument (Enochs, Smith, & Huinker, 2000), the

Teacher Self-Efficacy Scale (Tschannen-Moran & Woolfolk Hoy, 2001) was initially designed

to be a general, rather than subject-specific, measure. With minor edits to focus more

specifically on mathematics, (i.e., changing “school work” to “math”), the self-efficacy for

student engagement and self-efficacy for instructional strategies scales correlate significantly

with the scale designed to be subject specific (rSESE-SETM = .426, p = .001, rSEIS-SETM = .513, p <

.001). Thus, the evidence presented here suggests that researchers interested in measuring


subject-specific efficacies can adapt the widely-used Teacher Self-Efficacy Scale rather than rely

on less well-known and less tested subject-specific scales, providing opportunities to link results

more widely across the study of teacher efficacy.

Mathematics Anxiety

The evaluation component of mathematics anxiety is particularly troubling when

considering practical implications of these findings. Teachers and students are both increasingly

evaluated and those evaluations carry higher stakes than ever before. Given the research that

suggests teachers are modeling their anxiety and that their students are learning from this

modeling (e.g., Beilock et al., 2010), the modeling of evaluation anxiety has the potential to be

detrimental not just in mathematics, but in other areas of assessment. Teacher education

programs need to consider how to incorporate instruction around evaluation and evaluation

anxiety into coursework. In doing research on their own practice, mathematics methods teachers

have demonstrated that mathematics content anxiety can be reduced when teachers are mindful

about how they present material in their courses (e.g., McGlynn-Stewart, 2010; Vinson, 2001);

perhaps assessment teachers should begin to consider how they can similarly be mindful of their

own teaching in order to reduce student anxiety and begin to build a research literature around

most effective methods of reducing evaluation anxiety.


The lack of reliability of the student and mathematics expectancy scales is interesting in

that a lack of internal consistency in these scales suggests that either a) the items within a scale

measure very different constructs or b) the students are not consistent in how they feel about the

content of the scales. For the student scale, it appears that teacher education students are

inconsistent about what effects they expect the relationship between teachers and students to


have on student achievement. For example, they believe students have control of their own

motivation as it relates to their achievement, but they also believe that teachers are responsible

for students’ achievement even when low achievement reflects motivational issues. Perhaps this

scale will become more consistent once these students have experiences with their own students

in classrooms (i.e., mastery experiences), but it may be a very real finding that teachers and

teacher education students are ambivalent about when achievement is under their control and

when it is under student control. There are likely aspects of individual teacher-student

relationships that could help explain this lack of consistency and should be studied further in

other research.

Both scales also decrease in internal consistency following exposure to the learning

blocks (as opposed to other scales which became more consistent). This is an interesting finding

in that aspects of the learning blocks may affect some beliefs about student and content more

than others for some students. The lack of consistency makes interpreting any changes difficult

(i.e., the scales do not function as intended). Thus, it may be useful to explore student and

content expectations more thoroughly in a qualitative way in order to better craft scales that can

capture general beliefs and change in these variables across time.

In terms of mathematics, the expectations for mathematics were inconsistent, but also

interesting for this population of students. Recall that these students were primarily interested in

teaching science, and thus, were more likely to have at least some mathematics background in

comparison to the full population of elementary teacher education students. They may value

their own past success (or at least lack of failure) in mathematics as being due to high levels of

effort in a subject that is perceived to be more difficult, but ultimately more logical than other

subjects, and at the same time they feel students generally dislike and worry about mathematics,


which will put pressure on them as teachers to maintain and improve student engagement in

content.

Limitations

Several important limitations exist in this study. First, recruitment resulted in a fairly

homogenous sample, with primarily teacher education students interested in teaching early and

upper elementary grades. This led to difficulty in assessing hypotheses about grade level

preference, and limited the generalizability of findings to elementary education majors.

Moreover, the target audience of Algebra Ready materials is upper elementary and middle school

teachers. While students in this study found the materials useful, further research needs to be

done to assess the utility of materials for students interested in teaching middle school. Some

amelioration to the threat to the generalizability of learning block feedback may exist in that the

specific learning blocks chosen for students to review focused on development of conceptual

understandings important for teachers across elementary and middle school grades.

A second limitation is the design, which allowed for selection bias. Students chose

whether to respond to recruitment ads, leading to the theoretically-grounded possibility that

students with the highest self-efficacy around mathematics and the lowest anxiety for

mathematics were most likely to agree to participate. Attempts were made to decrease this

possibility by ensuring that recruitment materials made clear that there would be no evaluation of

actual mathematics skill as part of this project. However, the extent to which this was successful

is suspect given that nothing is known about the students who chose not to participate.

Further, of those agreeing to participate in the initial survey, only 42% agreed to continue

on to the learning blocks. Selection bias both into the study and into the learning blocks would

be hypothesized from self-efficacy theory, which asserts that task choice is a function of self-


efficacy. Further, the small effect size differences in self-efficacy to learn mathematics and self-

efficacy to teach mathematics between those students who chose to participate in the learning

blocks and those who did not supports this assertion.

The choice to focus on two learning blocks, both more conceptual in nature, is also a

limitation. Conceptual learning blocks were used in hopes that they would provide teacher

education students with content knowledge helpful for their mathematics methods courses, and

with the belief that learning blocks that focus more heavily on instructional activities may not be

useful for this population because they are not yet in classrooms. However, it is possible that

greater effects would have been found with one of the more practical learning blocks. Future

research should examine this possibility.

Additionally, this study focuses exclusively on self-report data, and thus, is open to

reporting biases and concomitant threats to validity. Students may have reported higher self-

efficacy and lower anxiety because of social desirability or demand characteristics that elicited

“good participant” behavior. For example, the support from faculty to recruit in their classrooms

as well as the generally helpful dispositions of the teacher education students may have

unintentionally biased students to respond in ways consistent with their beliefs about the desired

outcomes of this study.

Part of the study was to investigate evidence for future causal modeling approaches.

Given that the lack of experimental design, it is impossible to make causal conclusions.

Modeling approaches investigate prediction, but the directionality of any existing causality is

suspect and alternative models must be hypothesized and evaluated. Future work should attempt

to strengthen the causal argument to the extent that it is possible to randomly assign teachers and


students to voluntary professional development opportunities (not an easy task) or to create

quasi-experimental matched groups to investigate effects.

Finally, the greatest limitation of this study was the inability to determine the relationship

between self-efficacy and actual teaching behaviors. Given that these students are not yet in the

classroom, the outcome variable measured their interest and preference for teaching mathematics

content. While preference is indicative of task choice and motivation, it does not indicate how

effective these teachers will be in the classroom. It is entirely possible that teachers who

strongly dislike particular content areas do well in teaching them and that teachers who express

much enthusiasm for particular content fail to teach it well. Thus, future longitudinal work needs

to assess the impacts of efficacy beliefs as teachers move into classrooms, perhaps via

observation of in-class behaviors and measures of student motivational and achievement

outcomes.

Future Directions The results of this study open several avenues to future work. First, in terms of

mathematics anxiety, it is important to evaluate the extent to which mathematics anxiety can be

distinguished from evaluation anxiety. It may be that some students are simply more sensitive to

failure feedback and that little of the phenomenon of mathematics anxiety (at least in the

population of pre-service teachers) has to do with mathematics. If this is the case, it may be

more effective to support the resiliency of students in general than to target mathematics

specifically.

Teachers are increasingly expected to make data-driven decisions about their instruction.

This includes not only use of assessment data gathered by large-scale tests, but also appropriate

use of teacher-designed classroom assessment. Unfortunately, the anxiety measures in this study


did not include reference to use of student data, which is conceptually related to learning and

using mathematics. However, the statistics coursework item did elicit relatively high levels of

anxiety, suggesting a need to address teacher education students’ level of comfort with statistics

and use of statistics in their classrooms. Future research should explore teachers’ anxiety around

the use of assessment and student data.

Second, longitudinal work needs to be undertaken to better understand the developmental

trajectory of self-efficacy throughout teacher education and into the professional fields.

Evidence presented here suggests links between what teachers are most interested in teaching

and their efficacies, but work needs to be done to link preferences with actual teaching

behaviors. Further, results are suggestive that the students may have overly high efficacy beliefs

during their education programs. While it is important to help students feel efficacious,

unrealistic goals may lead to burnout once they enter the field. More needs to be done to

understand what appropriate levels of efficacy are at various times in the career.

Lastly, this study does not provide enough information about outcome expectancies

teachers may hold about themselves, their students, and the content they will be teaching. The

evidence presented from this study suggests the interaction between expectations is more

complex than could be captured by the instruments used here. Further review of the expectation

literature and qualitative work with teacher education students and in-service teachers is needed.

Conclusion

Although more must be done to fully model the relationships, this study provides

evidence of the predictive capacities of teacher efficacy models that incorporate student

experiences and feelings of anxiety to better understand task choice. Additionally, experience in

teacher education coursework has the potential to reduce anxiety for teaching. Finally, evidence


is provided that teacher professional development is not only perceived as useful to teacher

educations students, but has the potential to improve self-efficacy and reduce anxiety for

teaching. Given these findings, it makes sense to further evaluate the ways in which the

strengths of pre-service coursework and in-service professional development can be leveraged to

best prepare future teachers for their professional roles.


APPENDIX A: RECRUITMENT AND CONSENT DOCUMENTS

Initial Recruitment Email Hello, As a student interested in becoming a teacher, I am contacting you to ask if you are willing to help evaluate Algebra Ready professional development intended to help teachers improve their math instruction. We believe the feedback that teacher education students provide can help improve the professional development for pre-service and early career teachers. You will be asked to complete two surveys about your feelings about math and review two online math lessons (learning blocks). Your math skills will not be tested. The surveys and learning blocks should take you less than 3 hours; you will be paid for your time and thoughtful feedback. You may also find the materials helpful as you complete math methods coursework and start designing your own lessons. If you are interested in participating, please follow the link below to consent and complete the first survey. https://uarizona.co1.qualtrics.com/SE/?SID=SV_55xmX7ZlkP6SqJ7 (If this link fails to open, you may also copy and paste it into your browser.) You may email Amy Olson ([email protected]) or call 520-603-3956 with any questions or concerns. Please also contact Amy if you would like a copy of the final report. Thank you, Amy Olson, M.A. Algebra Ready Project

An Institutional Review Board responsible for human subjects research at The University of

Arizona reviewed this research project and found it to be acceptable, according to applicable

state and federal regulations and University policies designed to protect the rights and

welfare of participants in research.


Follow-Up Recruitment Email Hello again, If you have not yet had a chance, this is a reminder of an opportunity for teacher education students to participate in evaluation of real teacher professional development. We value the input of teacher education students in improving our lessons. If you choose to participate, you will be asked to complete two surveys and review two online math lessons (learning blocks). The surveys will ask about your feelings about math. Your math skills will not be tested, and you may find the lessons helpful as you take math methods courses and begin writing your own math lessons plans. Altogether, the tasks should take less than 3 hours, and you will be paid for your time. If you are interested in participating, please follow the link below to consent and complete the first survey. https://uarizona.co1.qualtrics.com/SE/?SID=SV_55xmX7ZlkP6SqJ7 (If this link fails to open, you may also copy and paste it into your browser.) You may email Amy Olson ([email protected]) or call 520-603-3956 with any questions or concerns. Please also contact Amy if you would like a copy of the final report. Thank you, Amy Olson. M.A. Algebra Ready Project

An Institutional Review Board responsible for human subjects research at The University of

Arizona reviewed this research project and found it to be acceptable, according to applicable

state and federal regulations and University policies designed to protect the rights and

welfare of participants in research.


Teacher Education Student Consent Form Project Title: Algebra Ready: Transitioning to Academic Success Study Investigator: Amy Olson, M.A. Project Principal Investigator: Thomas Good, Ph.D. This is a consent form for research participation. Please consider the information about this study carefully. Feel free to discuss the study with others and to ask questions before making your decision whether or not to participate. Why is this study being done? The purpose of this study is to improve online professional development content for the instruction of rational numbers and early algebra concepts and to learn more about how teacher education students view math. What will happen if I take part in this study? You will be asked to take two surveys about how you feel about math and math instruction. You will be asked to review two online professional development lessons (learning blocks). You will be asked to give your feedback about your experience with the learning blocks. Participation is voluntary. You may choose not to participate without penalty or loss of benefits to which you are otherwise entitled. You may discontinue participation at any time without penalty or loss of benefits. By agreeing to participate, you do not give up any personal legal rights you may have. What benefits can I expect from being in the study? You will potentially benefit from learning more pedagogical and content knowledge from the professional development. What risks can I expect from being in the study? The risks are minimal. You may be challenged to think about teaching and learning math in new ways. What are the costs of taking part in this study? You will spend approximately 3 hours participating in this study. Aside from your time, there are no costs for taking part. Will I be paid for taking part in this study? You will be compensated $50 for your 3 hours of participation. By law, payments to subjects may be considered taxable income. Your privacy will be protected. You will not be identified in any reports that result from this study. However, representatives of regulatory agencies, including the University of Arizona Human Subjects Protection Program, may review your records. Who can answer my questions about the study? For questions, concerns, complaints, or to be removed from this study at any time, you may contact Amy Olson ([email protected]) and 520-621-7828.


For questions about your rights as a participant in this study or to discuss other study-related concerns or complaints with someone who is not part of the research team, you may contact the Human Subjects Protection Program at 520-626-6721 or online at http://orcr.arizona.edu/hspp. Signing the consent form By electronically signing this form (typing my name), I affirm that I have read this form, and I am aware that I am being asked to participate in a research study. I have had the opportunity to ask questions and have had them answered to my satisfaction. I voluntarily agree to participate in this study. I do not give up any legal rights by signing this form. ___________________________________________ Student’s Name (typed) An Institutional Review Board responsible for human subjects research at The University of Arizona reviewed this research project and found it to be acceptable, according to applicable state and federal regulations and University policies designed to protect the rights and welfare of participants in research.


APPENDIX B: COMPLETE INSTRUMENTATION

Learning Block Review Items

The following previously approved items are embedded in the learning blocks. Teacher education students will have the opportunity to complete them as they complete the blocks. A. In your opinion, what were the two or three most helpful ideas that were presented in this learning block? B. What are one or two things you will do with this information? C. Is there anything else you would like to know? D. Additional comments or suggestions? 1. Is the material presented in this learning block useful to you? Not useful Rarely useful Somewhat useful Useful Very useful 2. Does this material provide content that would be useful to experienced in-service teachers (with more than five years of experience)? Not useful Rarely useful Somewhat useful Useful Very useful


3. Does this learning block provide content that would be useful to new teachers in their first 1-3 years of teaching? Not useful Rarely useful Somewhat useful Useful Very useful 4. Does this learning block provide content that would be useful to pre-service teachers? Not useful Rarely useful Somewhat useful Useful Very useful 5. Would you classify the material in this learning block as: Review of material you have learned in other formats? New material you are just now learning? A combination of new and review material? 6. To what extent do these materials overlap with other professional development opportunities you have had? No overlap Very little overlap Some overlap A lot of overlap Completely overlaps other professional development 7. If you answered that this learning block overlaps other professional development programs, please list those programs here:


Survey

Please provide your preferred email address so that we can contact you to give you access to the learning blocks and arrange payment. Preferred Email Address: _________________________________ This questionnaire is designed to help us gain a better understanding of the kinds of things that create difficulties for teachers in their school activities. Please indicate your opinion about each of the statements below. Your answers are confidential. Nothing Very

little Some

influence Quite a

bit A great

deal 1. How much will you be able to do to motivate students who show low interest in math schoolwork?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

2. How much will you be able to do to get students to believe they can do well in math schoolwork?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

3. How much will you be able to do to help your students value math learning?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

4. To what extent will you be able to craft good math questions for your students?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐


Nothing Very little

Some influence

Quite a bit

A great deal

5. How much will you be able to use a variety of assessment strategies in math?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

6. To what extent will you be able to provide an alternative explanation or example when students are confused about math?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

7. How much will you be able to assist families in helping their children do well in math?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

8. How well will you be able to implement alternative math strategies in your classroom?

☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐

Please indicate the degree to which you agree or disagree with each statement. Strongly

Agree Agree Uncertain Disagree Strongly

Disagree 1. When a student does better than usual in math, it is often because the teacher exerted a little extra effort.

☐ ☐ ☐ ☐ ☐

2. I will continually find better ways to teach math.

☐ ☐ ☐ ☐ ☐

3. Even if I try very hard, I will not teach math as well as I will most subjects.

☐ ☐ ☐ ☐ ☐

4. When the math grades of students improve, it is often due to their teacher having found a more effective teaching approach.

☐ ☐ ☐ ☐ ☐


Strongly Agree

Agree Uncertain Disagree Strongly Disagree

5. Math requires more effort than other subjects. ☐ ☐ ☐ ☐ ☐ 6. I will know the steps necessary to teach math concepts effectively. ☐ ☐ ☐ ☐ ☐

7. I will not be very effective in monitoring math activities. ☐ ☐ ☐ ☐ ☐

8. If students are underachieving in math, it is most likely due to ineffective math teaching.

☐ ☐ ☐ ☐ ☐

9. I will generally teach math ineffectively. ☐ ☐ ☐ ☐ ☐

10. Math makes more sense than other subjects.

☐ ☐ ☐ ☐ ☐

11. The inadequacy of a student’s math background can be overcome by good teaching.

☐ ☐ ☐ ☐ ☐

12. The low math achievement of some students cannot generally be blamed on their teachers.

☐ ☐ ☐ ☐ ☐

13. When a low-achieving child progresses in math, it is usually due to extra attention given by the teacher.

☐ ☐ ☐ ☐ ☐

14. I will understand math concepts well enough to be effective in teaching elementary math.

☐ ☐ ☐ ☐ ☐

15. It is more difficult to improve in math than in other subjects.

☐ ☐ ☐ ☐ ☐

16. Increased effort in math teaching produces little change in some students’ math achievement.

☐ ☐ ☐ ☐ ☐

17. The teacher is generally responsible for the achievement of students in math.

☐ ☐ ☐ ☐ ☐


Strongly Agree

Agree Uncertain Disagree Strongly Disagree

18. Students’ achievement in math is directly related to their teachers’ effectiveness in math teaching. ☐ ☐ ☐ ☐ ☐

19. If parents comment that their child is showing more interest in math at school, it is probably due to the performance of the child’s teacher.

☐ ☐ ☐ ☐ ☐

20. In general, people worry more about being successful in math than they do in other subjects.

☐ ☐ ☐ ☐ ☐

21. I will find it difficult to use manipulatives to explain to students why math works.

☐ ☐ ☐ ☐ ☐

22. I will typically be able to answer students’ math questions.

☐ ☐ ☐ ☐ ☐

23. I wonder if I have the necessary skills to teach math.

☐ ☐ ☐ ☐ ☐

24. Effectiveness in math teaching has little influence on the achievement of students with low motivation.

☐ ☐ ☐ ☐ ☐

25. In general, people like taking math more than other subjects.

☐ ☐ ☐ ☐ ☐

26. Given a choice, I will not invite the principal to evaluate my math teaching.

☐ ☐ ☐ ☐ ☐

27. When a student has difficulty understanding a math concept, I will usually be at a loss as to how to help the student understand it better.

☐ ☐ ☐ ☐ ☐

28. When teaching math, I will usually welcome student questions.

☐ ☐ ☐ ☐ ☐

29. I will not know what to do to turn students onto math. ☐ ☐ ☐ ☐ ☐

30. Even teachers with good math teaching abilities cannot help some kids learn. ☐ ☐ ☐ ☐ ☐


Please indicate your level of anxiety in the following situations. Not at

all A little A fair

amount Much Very

much 1. Looking through the pages in a math text ☐ ☐ ☐ ☐ ☐ 2. Having to use the tables in the back of a math book

☐ ☐ ☐ ☐ ☐

3. Thinking about an upcoming math test one day before ☐ ☐ ☐ ☐ ☐

4. Watching a teacher work an algebraic equation on the blackboard ☐ ☐ ☐ ☐ ☐

5. Being told how to interpret probability statements ☐ ☐ ☐ ☐ ☐

6. Picking up a math textbook to begin working on a homework assignment

☐ ☐ ☐ ☐ ☐

7. Taking an examination (quiz) in a math course

☐ ☐ ☐ ☐ ☐

8. Reading or interpreting graphs or charts ☐ ☐ ☐ ☐ ☐

9. Signing up for a course in statistics ☐ ☐ ☐ ☐ ☐

10. Waiting to get a math test returned in which you expected to do well ☐ ☐ ☐ ☐ ☐

11. Being given a “pop” quiz in math class

☐ ☐ ☐ ☐ ☐

12. Walking on campus and thinking about a math course

☐ ☐ ☐ ☐ ☐

13. Looking through the pages in your math series teachers’ manual

☐ ☐ ☐ ☐ ☐

14. Teaching students how to use and interpret tables, graphs, and charts ☐ ☐ ☐ ☐ ☐

15. Preparing students for a “standardized” math test throughout the week before ☐ ☐ ☐ ☐ ☐


Not at all

A little A fair amount

Much Very much

16. Working out math equations on the board in front of a class of students ☐ ☐ ☐ ☐ ☐

17. Preparing to teach students a new math concept that will be challenging for them ☐ ☐ ☐ ☐ ☐

18. Explaining the rationale for the math curriculum to a parent who stopped by your classroom after school

☐ ☐ ☐ ☐ ☐

19. Talking to a student who wanted to use a different way to solve a math problem than the way you taught in class

☐ ☐ ☐ ☐ ☐

20. Writing a lesson plan for teaching a new math concept ☐ ☐ ☐ ☐ ☐

21. Waiting for results of your students’ year-end math tests ☐ ☐ ☐ ☐ ☐

22. Having a surprise evaluation by an administrator during a math lesson you are teaching

☐ ☐ ☐ ☐ ☐

23. Walking into school and thinking about teaching a math lesson ☐ ☐ ☐ ☐ ☐

Please rank the following core subject areas in the order you are most confident (least worried) about teaching them (1 = most confident, 4 = least confident). ________ English Language Arts

________ Math ________ Science

________ Social Studies


What classroom experiences have you had? (Select all that apply.)

☐ I have taken math classes like the ones I expect to teach. ☐ I have observed classroom teachers give math lessons in the grade(s) I want to teach. ☐ I have observed teacher education faculty give math lessons similar to the ones I expect to teach. ☐ I have participated in workshops or professional development about teaching math. ☐ I have designed math lessons.

☐ I have student teacher experience assisting a mentor teacher with math lessons. ☐ I have student teaching experience giving my own math lessons. What grade level do you most wish to teach?

☐ Pre-Kindergarten or Kindergarten

☐ Grades 1 – 2

☐ Grades 3 – 4

☐ Grades 5 – 6

☐ Grades 7 – 8

☐ High School


Thank you for your interest in the project! If you provided your email address, you will receive a follow up invite to evaluate the Algebra Ready lessons and to arrange payment. If you have chosen not to participate, thank you for considering this opportunity. If you change your mind, please do not hesitate to contact Amy Olson ([email protected])


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